%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "3.22", %%% date = "27 March 2009", %%% time = "07:55:14 MST", %%% filename = "elefunt.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "39110 18847 83023 790157", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "BibTeX; bibliography; elementary functions; %%% special functions", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications about %%% the computation of the elementary functions %%% (square root, exponential, logarithm, %%% trigonometric, inverse trigonometric, %%% hyperbolic, inverse hyperbolic, ...), and %%% some selected special functions (Bessel, %%% exponential integral, Gamma, log-Gamma, psi, %%% ...) , in computer programming languages. %%% %%% At version 3.22, the year coverage looked %%% like this: %%% %%% 1925 ( 1) 1954 ( 2) 1983 ( 20) %%% 1926 ( 0) 1955 ( 1) 1984 ( 13) %%% 1927 ( 0) 1956 ( 0) 1985 ( 15) %%% 1928 ( 0) 1957 ( 4) 1986 ( 17) %%% 1929 ( 0) 1958 ( 4) 1987 ( 24) %%% 1930 ( 0) 1959 ( 6) 1988 ( 35) %%% 1931 ( 0) 1960 ( 9) 1989 ( 62) %%% 1932 ( 0) 1961 ( 5) 1990 ( 16) %%% 1933 ( 0) 1962 ( 0) 1991 ( 27) %%% 1934 ( 0) 1963 ( 5) 1992 ( 17) %%% 1935 ( 0) 1964 ( 5) 1993 ( 22) %%% 1936 ( 0) 1965 ( 5) 1994 ( 29) %%% 1937 ( 0) 1966 ( 7) 1995 ( 22) %%% 1938 ( 0) 1967 ( 3) 1996 ( 12) %%% 1939 ( 0) 1968 ( 7) 1997 ( 16) %%% 1940 ( 0) 1969 ( 8) 1998 ( 7) %%% 1941 ( 0) 1970 ( 5) 1999 ( 31) %%% 1942 ( 0) 1971 ( 15) 2000 ( 23) %%% 1943 ( 1) 1972 ( 15) 2001 ( 17) %%% 1944 ( 2) 1973 ( 9) 2002 ( 8) %%% 1945 ( 2) 1974 ( 8) 2003 ( 12) %%% 1946 ( 1) 1975 ( 11) 2004 ( 20) %%% 1947 ( 0) 1976 ( 11) 2005 ( 13) %%% 1948 ( 1) 1977 ( 6) 2006 ( 7) %%% 1949 ( 0) 1978 ( 13) 2007 ( 6) %%% 1950 ( 0) 1979 ( 13) 2008 ( 1) %%% 1951 ( 3) 1980 ( 11) 2009 ( 2) %%% 1952 ( 3) 1981 ( 15) %%% 1953 ( 1) 1982 ( 27) %%% %%% Article: 459 %%% Book: 39 %%% InBook: 1 %%% InCollection: 19 %%% InProceedings: 118 %%% Manual: 1 %%% MastersThesis: 3 %%% Misc: 3 %%% PhdThesis: 13 %%% Proceedings: 43 %%% TechReport: 39 %%% Unpublished: 1 %%% %%% Total entries: 739 %%% %%% This bibliography has been collected from %%% bibliographies in the author's personal %%% files, from the OCLC WorldCat and %%% Contents1st databases, from the American %%% Mathematical Society MathSciNet database, %%% from the ACM Computing Archive CD-ROM, %%% and from the computer science bibliography %%% collection on ftp.ira.uka.de in %%% /pub/bibliography to which many people of %%% have contributed. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% BibTeX citation tags are uniformly chosen as %%% name:year:abbrev, where name is the family %%% name of the first author or editor, year is a %%% 4-digit number, and abbrev is a 3-letter %%% condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% This bibliography is sorted by year, and %%% within each year, by author and title key, %%% using ``bibsort -byyear''. Cross-referenced %%% proceedings entries appear at the end, %%% because of a restriction in the current %%% BibTeX. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== %%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here. %%% The more conventional undelimited form \toenglish{...} has braces %%% that prevent BibTeX's downcasing operation, and the alternate form %%% {\toenglish{...}} is considered a `special character' by BibTeX, %%% and all of {...} gets downcased. We avoid the name \english to %%% prevent conflicts with language options in packages like Babel. %%% %%% To suppress output of English translations of non-English titles, %%% use %%% "\def \toenglish #1\endtoenglish{\unskip}" %%% instead. %%% %%% Alternative Cyrillic definitions are supplied in the event that %%% cyracc.def is not loaded. @Preamble{"\input bibnames.sty" # "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " # "\ifx \undefined \cyr \let \cyr = \relax \fi " # "\ifx \undefined \cdprime \def \cdprime{''} \fi " # "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" # "\hyphenation{ Rich-ard }" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} @String{ack-nj= "Norbert Juffa, 2445 Mission College Blvd., Santa Clara, CA 95054, USA, e-mail: \path|norbert@@iit.com|"} @String{ack-rfb= "Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: \path=boisvert@cam.nist.gov="} %%% ==================================================================== %%% Institution abbreviations: @String{inst-ANL= "Argonne National Laboratory"} @String{inst-ANL:adr= "9700 South Cass Avenue, Argonne, IL 60439-4801, USA"} @String{inst-CPAM-UCB= "Center for Pure and Applied Mathematics, University of California, Berkeley"} @String{inst-CPAM-UCB:adr= "Berkeley, CA, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACTA-INFO= "Acta Informatica"} @String{j-ADV-APPL-MATH= "Advances in Applied Mathematics"} @String{j-AM-J-MATH= "American Journal of Mathematics"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-ANN-MATH-ARTIF-INTELL= "Annals of Mathematics and Artificial Intelligence"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-AUSTRALIAN-J-PHYS= "Australian Journal of Physics"} @String{j-AUTOMATICA= "Automatica: the journal of IFAC, the International Federation of Automatic Control"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-C-R-ACAD-BULGARE-SCI= "Comptes rendus de l'Acad{\'e}mie bulgare des sciences"} @String{j-CACM= "Communications of the ACM"} @String{j-CCCUJ= "C/C++ Users Journal"} @String{j-COMP-MATH-APPL-B= "Computers and Mathematics with Applications. Part B"} @String{j-COMP-J= "The Computer Journal"} @String{j-COMPUT-STAT-DATA-ANAL= "Computational Statistics \& Data Analysis"} @String{j-COMPUTER= "Computer"} @String{j-COMPUTING= "Computing: Archiv fur informatik und numerik"} @String{j-COMPUTING-SUPPLEMENTUM= "Computing. Supplementum"} @String{j-CONST-APPROX= "Constructive Approximation"} @String{j-DDJ= "Dr. Dobb's Journal of Software Tools"} @String{j-ELECT-LETTERS= "Electronics Letters"} @String{j-ELEK-RECHENANLAGEN= "Elektronische Rechenanlagen"} @String{j-IBM-JRD= "IBM Journal of Research and Development"} @String{j-IBM-SYS-J= "IBM Systems Journal"} @String{j-IEE-PROC-COMPUT-DIGIT-TECH= "IEE Proceedings. Computers and Digital Techniques"} @String{j-IEEE-J-SOLID-STATE-CIRCUITS= "IEEE Journal of Solid-State Circuits"} @String{j-IEEE-SIGNAL-PROCESS-LETT= "IEEE signal processing letters"} @String{j-IEEE-TRANS-CIRCUITS-SYST-2= "IEEE transactions on circuits and systems. 2, Analog and digital signal processing"} @String{j-IEEE-TRANS-COMPUT= "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-INF-THEORY= "IEEE Transactions on Information Theory"} @String{j-IEEE-TRANS-SIG-PROC= "IEEE Transactions on Signal Processing"} @String{j-IEEE-TRANS-VLSI-SYST= "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"} @String{j-IJQC= "International Journal of Quantum Chemistry"} @String{j-IJSAHPC= "The International Journal of Supercomputer Applications and High Performance Computing"} @String{j-INFO-PROC-LETT= "Information Processing Letters"} @String{j-INT-J-COMPUT-INF-SCI= "International Journal of Computer and Information Sciences"} @String{j-INT-J-MATH-EDU-SCI-TECH= "International journal of mathematical education in science and technology"} @String{j-INT-J-MATH-MATH-SCI= "International Journal of Mathematics and Mathematical Sciences"} @String{j-INTEGRATION-VLSI-J= "Integration, the VLSI journal"} @String{j-INTEL-TECH-J= "Intel Technology Journal"} @String{j-INTERVAL-COMP= "Interval Computations = Interval'nye vychisleniia"} @String{j-J-ACM= "Journal of the Association for Computing Machinery"} @String{j-J-ALG= "Journal of Algorithms"} @String{j-J-APPROX-THEORY= "Journal of Approximation Theory"} @String{j-J-COMP-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPLEXITY= "Journal of complexity"} @String{j-J-COMPUT-PHYS= "Journal of Computational Physics"} @String{j-J-MULTIVAR-ANAL= "Journal of multivariate analysis"} @String{j-J-PAR-DIST-COMP= "Journal of Parallel and Distributed Computing"} @String{j-J-PHYS-A= "Journal of Physics A (Mathematical and General)"} @String{j-J-STAT-COMPUT-SIMUL= "Journal of Statistical Computation and Simulation"} @String{j-J-STAT-SOFT= "Journal of Statistical Software"} @String{j-J-SYMBOLIC-COMP= "Journal of Symbolic Computation"} @String{j-J-SYMBOLIC-LOGIC= "Journal of Symbolic Logic"} @String{j-J-UCS= "J.UCS: The Journal of Universal Computer Science"} @String{j-J-VLSI-SIGNAL-PROC= "Journal of VLSI Signal Processing"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LIN-MULT-ALGEBRA= "Linear and Multilinear Algebra"} @String{j-LOGIN= ";login: the USENIX Association newsletter"} @String{j-MATH-COMP= "Mathematics of Computation"} @String{j-MATH-COMP-SIM= "Mathematics and Computers in Simulation"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-MATH-MODEL-NUM-ANA= "Mathematical modelling and numerical analysis = Modelisation math{\'e}matique et analyse num{\'e}rique: $M^2AN$"} @String{j-MATH-OP-RES= "Mathematics of Operations Research"} @String{j-MATH-PROG= "Mathematical Programming"} @String{j-MATH-TABLES-AIDS-COMPUT= "Mathematical Tables and Aids to Computation"} @String{j-MATH-TABLES-OTHER-AIDS-COMPUT= "Mathematical Tables and Other Aids to Computation"} @String{j-MICROPROC-MICROPROG= "Microprocessing and Microprogramming"} @String{j-MICROPROC-MICROSYS= "Microprocessors and Microsystems"} @String{j-NACH-ELEK= "Nachrichtentechnik Elektronik"} @String{j-NEURAL-COMP= "Neural Computation"} @String{j-NEURAL-NETWORKS= "Neural Networks"} @String{j-NORDISK-TIDSKR-INFORM-BEHAND= "Nordisk tidskrift for informationsbehandling"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUCL-INSTR-METH= "Nuclear Instruments and Methods"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-OPER-RES= "Operations Research"} @String{j-PAC-J-MATH= "Pacific Journal of Mathematics"} @String{j-PARALLEL-COMPUTING= "Parallel Computing"} @String{j-PHYS-TODAY= "Physics Today"} @String{j-PHYSICA-D= "Physica D"} @String{j-PROC-AM-MATH-SOC= "Proceedings of the American Mathematical Society"} @String{j-PROG-COMP-SOFT= "Programming and Computer Software; translation of Programmirovaniye (Moscow, USSR) Plenum"} @String{j-PROGRAMMIROVANIE= "Programmirovanie"} @String{j-RUSS-J-MATH-PHYS= "Russian Journal of Mathematical Physics"} @String{j-SIAM-J-APPL-MATH= "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-CONTROL-OPTIM= "SIAM Journal on Control and Optimization"} @String{j-SIAM-J-MAT-ANA-APPL= "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-MATH-ANA= "SIAM journal on mathematical analysis"} @String{j-SIAM-J-NUM-ANALYSIS-B= "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGADA-LETTERS= "ACM SIGADA Ada Letters"} @String{j-SIGNUM= "ACM SIGNUM Newsletter"} @String{j-SIGPLAN= "ACM SIGPLAN Notices"} @String{j-TECHNIQUE-SCI-INFORMATIQUES= "Technique et Science Informatiques"} @String{j-THEOR-COMP-SCI= "Theoretical Computer Science"} @String{j-TOKYO-J-MATH= "Tokyo journal of mathematics"} @String{j-TOMS= "ACM Transactions on Mathematical Software"} @String{j-TRANS-AM-MATH-SOC= "Transactions of the American Mathematical Society"} @String{j-TRANS-SOC-COMP-SIM= "Transactions of the Society for Computer Simulation"} @String{j-Z-ANAL-ANWEND= "Zeitschrift f{\"u}r Analysis und ihre Anwendungen"} @String{j-Z-MATH-LOGIK-GRUNDL-MATH= "Zeitschrift f{\\\"u}r mathematische Logik und Grundlagen der Mathematik"} %%% ==================================================================== %%% Publishers and their addresses: @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AFIPS= "AFIPS Press"} @String{pub-AFIPS:adr= "Montvale, NJ, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-AP= "Academic Press"} @String{pub-AP:adr= "New York, NY, USA"} @String{pub-BIRKHAUSER= "Birkh{\"a}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-CHAPMAN-HALL= "Chapman and Hall, Ltd."} @String{pub-CHAPMAN-HALL:adr= "London, UK"} @String{pub-CHAPMAN-HALL-CRC= "Chapman and Hall/CRC"} @String{pub-CHAPMAN-HALL-CRC:adr= "Boca Raton, FL, USA"} @String{pub-CLARENDON-PRESS= "Clarendon Press"} @String{pub-CLARENDON-PRESS:adr= "Oxford, UK"} @String{pub-CRC= "CRC Press"} @String{pub-CRC:adr= "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-ELLIS-HORWOOD= "Ellis Horwood"} @String{pub-ELLIS-HORWOOD:adr= "New York, NY, USA"} @String{pub-ENH= "Elsevier North-Holland, Inc."} @String{pub-ENH:adr= "New York, NY, USA"} @String{pub-IBM= "IBM Corporation"} @String{pub-IBM:adr= "San Jose, CA, USA"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers"} @String{pub-KLUWER:adr= "Dordrecht, The Netherlands"} @String{pub-MCGRAW-HILL= "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr= "New York, NY, USA"} @String{pub-NIST= "National Institute for Standards and Technology"} @String{pub-NIST:adr= "Gaithersburg, MD, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PERGAMON= "Pergamon Press"} @String{pub-PERGAMON:adr= "New York, NY, USA"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Englewood Cliffs, NJ 07632, USA"} @String{pub-REK= "Robert E. Krieger Publishing Company"} @String{pub-REK:adr= "Huntington, NY, USA"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SPIE= "Society of Photo-optical Instrumentation Engineers (SPIE)"} @String{pub-SPIE:adr= "Bellingham, WA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-TEUBNER= "Teubner"} @String{pub-TEUBNER:adr= "Stuttgart, Leipzig"} @String{pub-USENIX= "USENIX"} @String{pub-USENIX:adr= "San Francisco, CA, USA"} @String{pub-WCB= "William C. Brown Company Publishers"} @String{pub-WCB:adr= "Dubuque, IA, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LNCS= "Lecture Notes in Computer Science"} %%% ==================================================================== %%% Bibliography entries, sorted by year and citation label: @Article{Ritt:1925:EFT, author = "J. F. Ritt", title = "Elementary functions and their inverses", journal = j-TRANS-AM-MATH-SOC, volume = "27", number = "1", pages = "68--90", year = "1925", CODEN = "TAMTAM", ISSN = "0002-9947", MRclass = "30A05 (33B10)", MRnumber = "MR1501299", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", } @Article{RCA:1943:TTF, author = "{R. C. A.}", title = "Tables of Trigonometric Functions in Non-Sexagesimal Arguments", journal = j-MATH-TABLES-AIDS-COMPUT, volume = "1", number = "2", pages = "33--44", month = apr, year = "1943", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", note = "Original journal has only `R. C. A.' as author: possibly R. C. Archibald.", acknowledgement = ack-nhfb, } @Article{Bateman:1944:GTB, author = "Harry Bateman and Raymond Clare Archibald", title = "A Guide to Tables of {Bessel} Functions", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "1", number = "7", pages = "205--308", month = jul, year = "1944", CODEN = "MTTCAS", ISSN = "0891-6837", MRclass = "", MRnumber = "6,132b", MRreviewer = "G. Szeg{\"o}", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{DHL:1944:NCB, author = "{D. H. L.}", title = "Note on the Computation of the {Bessel} Function ${I}_n({X})$", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "1", number = "5", pages = "133--135", month = apr, year = "1944", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", note = "Original journal has only `D. H. L.' as author: probably D. H. Lehmer.", acknowledgement = ack-nhfb, } @Article{Abramowitz:1945:ZCB, author = "Milton Abramowitz", title = "Zeros of certain {Bessel} functions of fractional order", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "1", number = "9", pages = "353--354", month = jan, year = "1945", CODEN = "MTTCAS", ISSN = "0891-6837", MRclass = "65.0X", MRnumber = "6,132c", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Emde:1945:TEF, author = "Fritz Emde", title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]", publisher = "Edwards Bros.", address = "Ann Arbor, MI, USA", pages = "xii + 181", year = "1945", LCCN = "????", bibdate = "Fri Jun 11 12:34:09 1999", note = "Original edition published in 1940.", acknowledgement = ack-nhfb, } @Article{Anonymous:1946:MZC, author = "Anonymous", title = "More Zeros of Certain {Bessel} Functions of Fractional Order", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "2", number = "15", pages = "118--119", month = jul, year = "1946", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Emde:1948:TEF, author = "Fritz Emde", title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]", publisher = pub-TEUBNER, address = pub-TEUBNER:adr, edition = "Second", pages = "xii + 181", year = "1948", LCCN = "QA55 .E5 1948", MRclass = "65.0X", MRnumber = "11,263k", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Fogel:1951:FTE, author = "{\`E}. K. Fogel'", title = "A finite theory of elementary functions. {I}. Logarithmic and exponential functions. ({Russian})", journal = "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis", volume = "5", number = "46", pages = "801--813", year = "1951", MRclass = "33.0X", MRnumber = "15,218b", MRreviewer = "H. N. Shapiro", bibdate = "Sat Apr 25 13:05:19 1998", acknowledgement = ack-nhfb, } @Article{Salzer:1951:FCE, author = "H. E. Salzer", title = "Formulas for Calculating the Error Function of a Complex Variable", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "5", number = "34", pages = "67--70", month = apr, year = "1951", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Salzer:1951:RTT, author = "H. E. Salzer", title = "Radix Table for Trigonometric Functions and their Inverses to High Accuracy", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "5", number = "33", pages = "9--11", month = jan, year = "1951", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InBook{Goncarov:1952:EFC, author = "V. L. Gon{\v{c}}arov", booktitle = "Encyclopaedia of elementary mathematics. Book III. Functions and limits (the foundations of analysis)", title = "Elementary functions of a complex variable", publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.", address = "Moscow-Leningrad, USSR", pages = "491--552", year = "1952", MRclass = "30.0X", MRnumber = "14,1073c", MRreviewer = "R. P. Boas, Jr.", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Goncarov:1952:EFR, author = "V. L. Gon{\v{c}}arov", booktitle = "Encyclopaedia of elementary mathematics. Book III. Functions and limits (the foundations of analysis)", title = "Elementary functions of a real variable. Limits of sequences and functions. The general concept of a function", publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.", address = "Moscow-Leningrad, USSR", pages = "9--296", year = "1952", MRclass = "27.2X", MRnumber = "14,1070d", MRreviewer = "R. P. Boas, Jr.", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Kuipers:1952:PSE, author = "L. Kuipers", title = "Properties of some elementary functions", journal = "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes Math.", volume = "55", number = "14", pages = "388--393", year = "1952", MRclass = "27.0X", MRnumber = "14,360e", MRreviewer = "E. Frank", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Scherberg:1953:ACP, author = "Max G. Scherberg and John F. Riordan", title = "Analogue Calculation of Polynomial and Trigonometric Expansions (in {Other Aids to Computation})", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "7", number = "41", pages = "61--65", month = jan, year = "1953", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Clenshaw:1954:PAE, author = "C. W. Clenshaw", title = "Polynomial approximations to elementary functions", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "8", pages = "143--147", year = "1954", ISSN = "0891-6837", MRclass = "41.1X", MRnumber = "16,128f", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Book{Hastings:1955:ADC, author = "Cecil {Hastings, Jr.}", title = "Approximations for digital computers", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "viii + 201", year = "1955", ISBN = "0-691-07914-5", LCCN = "QA76 .H37", bibdate = "Mon Oct 01 15:59:48 2007", bibsource = "z3950.loc.gov:7090/Voyager", note = "Assisted by Jeanne T. Hayward and James P. Wong, Jr.", series = "The Rand series", acknowledgement = ack-nhfb, remark = "Reprinted 1957, 1959, 1962, 1966, and 1970. I have fourth printing (1962).", subject = "Electronic digital computers; Numerical analysis", } @Article{LaFara:1954:MCI, author = "Robert L. LaFara", title = "A Method for Calculating Inverse Trigonometric Functions", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "8", number = "47", pages = "132--139", month = jul, year = "1954", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Kogbetliantz:1957:CEN, author = "E. G. Kogbetliantz", title = "Computation of $e^N$ for $-\infty < N < +\infty$ Using an Electronic Computer", journal = j-IBM-JRD, volume = "1", number = "2", pages = "110--115", month = apr, year = "1957", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "68.0X", MRnumber = "19,775d", bibdate = "Tue Sep 06 20:55:54 1994", acknowledgement = ack-nhfb, reviewer = "W. F. Freiberger", } @Article{Linskii:1957:CEF, author = "V. S. Linski{\u{\i}}", title = "Calculation of elementary functions on automatic digital machines. ({Russian})", journal = "Vy{\v{c}}isl. Mat.", volume = "2", pages = "90--119", year = "1957", MRclass = "68.00", MRnumber = "21 \#982", MRreviewer = "J. W. Carr, III", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Luke:1957:C, author = "Yudell L. Luke", title = "On the Computation of $\log {Z}$ and ${\rm arc} \tan {Z}$", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "11", number = "57", pages = "16--18", month = jan, year = "1957", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Stegun:1957:GBF, author = "Irene A. Stegun and Milton Abramowitz", title = "Generation of {Bessel} Functions on High Speed Computers", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "11", number = "60", pages = "255--257", month = oct, year = "1957", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Goldstein:1958:BFL, author = "M. Goldstein and R. M. Thaler", title = "{Bessel} Functions for Large Arguments", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "12", number = "61", pages = "18--26", month = jan, year = "1958", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Kogbetliantz:1958:CANa, author = "E. G. Kogbetliantz", title = "Computation of Arctan {N} for $-\infty < {N} < +\infty$ Using an Electronic Computer", journal = j-IBM-JRD, volume = "2", number = "1", pages = "43--53", month = jan, year = "1958", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65.3X", MRnumber = "19,982e", bibdate = "Wed Aug 31 13:40:00 1994", acknowledgement = ack-nhfb, reviewer = "C. B. Haselgrove", } @Article{Kogbetliantz:1958:CANb, author = "E. G. Kogbetliantz", title = "Computation of Arcsin {N} for $0<{N}<1$ Using an Electronic Computer", journal = j-IBM-JRD, volume = "2", number = "3", pages = "218--222", month = jul, year = "1958", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65.3X", MRnumber = "19,1197c", bibdate = "Wed Aug 31 13:41:37 1994", acknowledgement = ack-nhfb, reviewer = "C. B. Haselgrove", } @Article{Wadey:1958:TSR, author = "W. G. Wadey", title = "Two Square-Root Approximations", journal = j-CACM, volume = "1", number = "11", pages = "13--14", month = nov, year = "1958", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed Jul 14 15:48:22 MDT 2004", bibsource = "http://portal.acm.org/; http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58", acknowledgement = ack-nhfb, oldlabel = "Wadey58", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58", } @Article{Davis:1959:LEI, author = "P. J. Davis", title = "{Leonhard Euler}'s integral: {A} historical profile of the gamma function: In Memoriam: {Milton Abramowitz}", journal = j-AMER-MATH-MONTHLY, volume = "66", number = "??", pages = "849--869", month = "????", year = "1959", CODEN = "AMMYAE", ISSN = "0002-9890", MRclass = "00 (33.00)", MRnumber = "MR0106810 (21 #5540)", bibdate = "Mon Nov 24 20:57:26 2008", acknowledgement = ack-nhfb, } @Article{Goldstein:1959:RTC, author = "M. Goldstein and R. M. Thaler", title = "Recurrence Techniques for the Calculation of {Bessel} Functions", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "13", number = "66", pages = "102--108", month = apr, year = "1959", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Kogbetliantz:1959:CSC, author = "E. G. Kogbetliantz", title = "Computation of $\sin{N}$, $\cos{N}$, and ${M}$th Root of ${N}$ Using an Electronic Computer", journal = j-IBM-JRD, volume = "3", number = "2", pages = "147--152", month = apr, year = "1959", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65.00", MRnumber = "21 \#964", bibdate = "Thu Sep 1 10:15:56 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb, reviewer = "B. A. Chartres", } @Article{Sarafyan:1959:NMC, author = "Diran Sarafyan", title = "A New Method of Computation of Square Roots Without Using Division", journal = j-CACM, volume = "2", number = "11", pages = "23--24", month = nov, year = "1959", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed Jul 14 15:48:24 MDT 2004", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/", note = "See comments \cite{Traub:1960:CNM}.", acknowledgement = ack-nhfb, oldlabel = "Sarafyan59", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59", } @Article{Sherry:1959:CGF, author = "M. E. Sherry and S. Fulda", title = "Calculation of Gamma Functions to High Accuracy (in {Technical Notes and Short Papers})", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "13", number = "68", pages = "314--315", month = oct, year = "1959", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Volder:1959:CCT, author = "Jack Volder", title = "The {CORDIC} Computing Technique", journal = "Proceedings of the Western Joint Computer Conference", pages = "257--261", year = "1959", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Article{Haimovici:1960:MRE, author = "Corina Haimovici", title = "A method of representing elementary functions in algebras of finite order. ({Romanian})", journal = "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i Sec{\c{t}} I. (N.S.)", volume = "6", pages = "507--515", year = "1960", MRclass = "26.00", MRnumber = "24 \#A1342", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Kogbetliantz:1960:GEF, author = "E. G. Kogbetliantz", title = "Generation of elementary functions", crossref = "Ralston:1960:MMD", pages = "7--35", year = "1960", MRclass = "68.00 (65.00)", MRnumber = "22 \#8681", MRreviewer = "J. C. P. Miller", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Manual{Maehly:1960:ACD, author = "Hans J. Maehly", title = "Approximations for the {Control Data 1604}", organization = "Institute for Advanced Study", address = "Princeton, NJ", pages = "ii + 44", day = "15", month = jan, year = "1960", bibdate = "Tue Nov 06 00:39:07 2007", URL = "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf", acknowledgement = ack-nhfb, keywords = "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$; $\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604", } @Article{Philip:1960:FI, author = "J. R. Philip", title = "The function inverfc $\theta$", journal = j-AUSTRALIAN-J-PHYS, volume = "13", number = "1", pages = "13--20", month = mar, year = "1960", CODEN = "AUJPAS", ISSN = "0004-9506", MRnumber = "22 \9626", bibdate = "Tue Sep 11 20:53:59 2007", abstract = "The function inverfc $\theta$ arises in certain differential equations when concentration is taken as an independent variable. It enters into a general method of exact solution of the concentration-dependent diffusion equation. An account is given of the properties of this function, and of its derivatives and integrals. The function\par $$B(\theta) = (2/\pi^{1/2}) \exp[-({\rm inverfc} \theta)^2]$$ \noindent is intimately connected with the first integral of inverfc $\theta$ and with its derivatives. Tables of inverfc $\theta$ and $B(\theta)$ are given.", acknowledgement = ack-nhfb, ZMnumber = "135.28302", } @Article{Sarafyan:1960:DCS, author = "Diran Sarafyan", title = "Divisionless computation of square roots through continued squaring", journal = j-CACM, volume = "3", number = "5", pages = "319--321", month = may, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782", MRclass = "65.00", MRnumber = "22\#8639", bibdate = "Fri Nov 25 18:19:26 MST 2005", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.acm.org/pubs/contents/journals/cacm/", acknowledgement = ack-nhfb, keywords = "$\sqrt(x)$; elementary functions", ZMreviewer = "M. Lotkin", } @Article{Sholander:1960:AEE, author = "Marlow Sholander", title = "Analytical expressions and elementary functions", journal = j-AMER-MATH-MONTHLY, volume = "67", pages = "213--214", year = "1960", CODEN = "AMMYAE", ISSN = "0002-9890", MRclass = "26.00", MRnumber = "22 \#9553", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Traub:1960:CNM, author = "J. F. Traub", title = "Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]", journal = j-CACM, volume = "3", number = "2", pages = "86--86", month = feb, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Nov 25 18:19:25 MST 2005", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/", note = "See \cite{Sarafyan:1959:NMC}.", acknowledgement = ack-nhfb, oldlabel = "Traub60", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60", } @Book{Warmus:1960:TEF, author = "Mieczys{\l}aw Warmus", title = "Tables of elementary functions", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "vii + 567", year = "1960", LCCN = "QA55 .W3 1960", MRclass = "65.05", MRnumber = "23 \#B1141", MRreviewer = "J. C. P. Miller", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "Pa\'nstwowe Wydawnictwo Naukowe, Warsaw. Separately bound table of proportional parts, 30 pp.", acknowledgement = ack-nhfb, } @Article{Barakat:1961:EIG, author = "Richard Barakat", title = "Evaluation of the Incomplete Gamma Function of Imaginary Argument by {Chebyshev} Polynomials", journal = j-MATH-COMPUT, volume = "15", number = "73", pages = "7--11", month = jan, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Froberg:1961:RCA, author = "Carl-Erik Fr{\"o}berg", title = "Rational {Chebyshev} Approximations of Elementary Functions", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "1", number = "4", pages = "256--262", month = dec, year = "1961", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933243", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:07 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4", note = "See erratum \cite{Froberg:1963:ERC}.", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Article{Spielberg:1961:ECF, author = "Kurt Spielberg", title = "Efficient Continued Fraction Approximations To Elementary Functions", journal = j-MATH-COMP, volume = "15", number = "76", pages = "409--417", month = oct, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65.20", MRnumber = "MR0134842 (24 \#B894)", MRreviewer = "M. E. Rose", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj # " and " # ack-nhfb, } @Article{Thacher:1961:ISR, author = "Henry C. {Thacher, Jr.}", title = "Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine", journal = j-MATH-COMPUT, volume = "15", number = "76", pages = "399--403", month = oct, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Werner:1961:CAG, author = "Helmut Werner and Robert Collinge", title = "{Chebyshev} Approximations to the Gamma Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "15", number = "74", pages = "195--197", month = apr, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Carlitz:1963:IEF, author = "L. Carlitz", title = "The Inverse of the Error Function", journal = j-PAC-J-MATH, volume = "13", number = "2", pages = "459--470", year = "1963", CODEN = "PJMAAI", ISSN = "0030-8730", bibdate = "Thu Sep 13 21:30:05 2007", URL = "http://pjm.math.berkeley.edu/pjm; http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1", acknowledgement = ack-nhfb, } @Article{Froberg:1963:ERC, author = "C.-E. Fr{\"o}berg", title = "Erratum: {``Rational Chebyshev Approximations of Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261, line 12]}", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "3", number = "1", pages = "68--68", month = mar, year = "1963", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01963538", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:07 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1", note = "See \cite{Froberg:1961:RCA}.", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Book{Ljusternik:1963:MVF, author = "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R. Janpol'ski{{\u{\i}}}", title = "{\cyr Matematicheski{\u{\i}}analiz. Vychislenie {\`e}lementarnykh funktsi{\u{\i}}}. [Mathematical analysis. Computation of the elementary functions]", publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.", address = "Moscow, USSR", pages = "247", year = "1963", MRclass = "65.25", MRnumber = "28 \#1733", MRreviewer = "John Todd", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Peuizulaev:1963:AEF, author = "{\v{S}}. I. Pe{\u{\i}}zulaev", title = "An approximation by elementary functions. ({Russian})", journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.", volume = "3", pages = "769--770", year = "1963", MRclass = "41.30", MRnumber = "28 \#398", MRreviewer = "D. D. Stancu", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Whittlesey:1963:IGF, author = "John R. B. Whittlesey", title = "Incomplete Gamma Functions for Evaluating {Erlang} Process Probabilities", journal = j-MATH-COMPUT, volume = "17", number = "81", pages = "11--17", month = jan, year = "1963", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Burgoyne:1964:GTF, author = "F. D. Burgoyne", title = "Generalized Trigonometric Functions (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "18", number = "86", pages = "314--316", month = apr, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Lanczos:1964:PAG, author = "C. Lanczos", title = "A Precision Approximation of the Gamma Function", journal = j-SIAM-J-NUM-ANALYSIS-B, volume = "1", number = "??", pages = "86--96", month = "????", year = "1964", ISSN = "0887-459X", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Morelock:1964:AAE, author = "J. C. Morelock", title = "{ACM} Algorithm 229: Elementary Functions by Continued Fractions", journal = j-CACM, volume = "7", number = "5", pages = "296", month = may, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:32:21 1994", acknowledgement = ack-nhfb, } @Article{Simauti:1964:AFS, author = "Takakazu Simauti", title = "Approximation formulas for some elementary functions", journal = "Comment. Math. Univ. St. Paul.", volume = "12", pages = "23--35", year = "1964", CODEN = "COMAAC", ISSN = "0010-258X", MRclass = "65.25", MRnumber = "28 \#5552", MRreviewer = "John Todd", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Wengert:1964:SAD, author = "R. E. Wengert", title = "A simple automatic derivative evaluation program", journal = j-CACM, volume = "7", number = "8", pages = "463--464", year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz", abstract = "A procedure for automatic evaluation of total and partial derivatives of arbitrary algebraic functions is presented. The numerical values of derivatives are computed without developing analytic expressions for the derivatives. The function is decomposed into a sequence of elementary expressions A library is provided for differentiating of elementary functions.", acknowledgement = ack-nhfb, keywords = "point algorithm; differentiation arithmetic; computer program.", referred = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a]; [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a]; [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a]; [Wilk64a].", } @Article{Fraser:1965:SMC, author = "W. Fraser", title = "A Survey of Methods for Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable", journal = j-J-ACM, volume = "12", number = "3", pages = "295--314", month = jul, year = "1965", CODEN = "JACOAH", DOI = "http://doi.acm.org/10.1145/321281.321282", ISSN = "0004-5411", bibdate = "Thu Nov 03 08:47:50 1994", abstract = "Methods are described for the derivation of minimax and near-minimax polynomial approximations. For minimax approximations techniques are considered for both analytically defined functions and functions defined by a table of values. For near-minimax approximations methods of determining the coefficients of the Fourier--Chebyshev expansion are first described. These consist of the rearrangement of the coefficients of a power polynomial, and also direct determination of the coefficients from the integral which defines them, or the differential equation which defines the function. Finally there is given a convenient modification of an interpolation scheme which finds coefficients of a near-minimax approximation without requiring numerical integration or the numerical solution of a system of equations.", acknowledgement = ack-nhfb, } @Article{Kazangapov:1965:REF, author = "A. N. Kazangapov", title = "Representation of elementary function in the system of residual classes. ({Russian})", journal = "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk", volume = "3", pages = "79--84", year = "1965", MRclass = "65.25", MRnumber = "33 \#5090", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Book{Lyusternik:1965:HCE, author = "L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpol'skii", title = "Handbook for Computing Elementary Functions", volume = "76", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "xiii + 251", year = "1965", LCCN = "QA221.L513", MRclass = "65.25", MRnumber = "32 \#584", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", note = "Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.", series = "International series of monographs on pure and applied mathematics", acknowledgement = ack-nhfb, } @Article{Maklovic:1965:IIC, author = "S. T. Maklovi{\v{c}}", title = "Investigation of integrals containing {Bessel} and elementary functions. ({Russian})", journal = "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.", volume = "82", pages = "75--81", year = "1965", MRclass = "33.25", MRnumber = "34 \#387", MRreviewer = "H. A. Lauwerier", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Medhurst:1965:EI, author = "R. G. Medhurst and J. H. Roberts", title = "Evaluation of the Integral ${I}_n(b) = \frac{2}{\pi} \int^\infty_0 \bigg(\frac{\sin x}{x}\bigg)^n \cos (bx) dx$", journal = j-MATH-COMPUT, volume = "19", number = "89", pages = "113--117", month = apr, year = "1965", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Filippi:1966:BEE, author = "S. Filippi", title = "{Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus} \toenglish {The Computation of Some Elementary Transcendental Functions by Means of the {Richardson} Algorithm} \endtoenglish", journal = j-COMPUTING, volume = "1", number = "??", pages = "127--132", month = "????", year = "1966", CODEN = "CMPTA2", ISSN = "0010-485X", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Glasser:1966:ESI, author = "M. L. Glasser", title = "Evaluation of Some Integrals Involving the $\psi$-Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "94", pages = "332--333", month = apr, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Jurimae:1966:KFT, author = "E. J{\"u}rim{\"a}e", title = "Kompleksmuutuja funktsioonide teooria. {I}: Elementaarsed funktsioonid. ({Estonian}) [Theory of functions of a complex variable. {I}: Elementary functions]", publisher = "Tartu Riiklik {\"U}likool", address = "Tartu, Estonia", pages = "131", year = "1966", MRclass = "30.00", MRnumber = "40 \#5827a", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Kogbetliantz:1966:GEF, author = "E. G. Kogbetliantz", title = "Generation of Elementary Functions", crossref = "Ralston:1960:MMD", pages = "7--35", year = "1966", bibdate = "Sat Dec 09 14:09:27 1995", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @TechReport{Kuki:1966:CAE, author = "H. Kuki", title = "Comments on the {ANL} Evaluation of the {OS\slash 360 FORTRAN} Math Function Library", type = "????", number = "SSD 169, C4773", institution = "SHARE Secretary Distribution", address = "????", pages = "47--53", year = "1966", bibdate = "Wed Feb 14 19:13:50 2007", acknowledgement = ack-nhfb, } @Article{Takenaga:1966:EIG, author = "Roy Takenaga", title = "On the Evaluation of the Incomplete Gamma Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "96", pages = "606--610", month = oct, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Thompson:1966:ESI, author = "Rory Thompson", title = "Evaluation of ${I}_n(b) = 2\pi^{-1} \int^\infty_0 \big(\frac{sin x}{x}\big) ^n \cos (bx) dx$ and of Similar Integrals (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "94", pages = "330--332", month = apr, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Cody:1967:CAN, author = "W. J. Cody and K. E. Hillstrom", title = "{Chebyshev} Approximations for the Natural Logarithm of the Gamma Function", journal = j-MATH-COMPUT, volume = "21", number = "98", pages = "198--203", month = apr, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Fettis:1967:MCI, author = "Henry E. Fettis", title = "More on the Calculation of the Integral ${I}_n(b) = \frac{2}{\pi}\int^\infty_0\big(\frac{\sin x}{x}\big)^n \cos bx dx$ (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "21", number = "100", pages = "727--730", month = oct, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Moody:1967:ADF, author = "William T. Moody", title = "Approximations for the Psi (Digamma) Function (in Technical Notes and Short Notices)", journal = j-MATH-COMPUT, volume = "21", number = "97", pages = "112--112", month = jan, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Fike:1968:CEM, author = "C. T. Fike", title = "Computer Evaluation of Mathematical Functions", publisher = pub-PH, address = pub-PH:adr, pages = "xii + 227", year = "1968", LCCN = "QA297 .F5", bibdate = "Thu Sep 1 10:12:51 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nj, } @Article{Galant:1968:HAG, author = "D. C. Galant and P. F. Byrd", title = "High Accuracy Gamma Function Values for Some Rational Arguments (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "22", number = "104", pages = "885--887", month = oct, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Hart:1968:CAa, author = "John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall", title = "Computer Approximations", publisher = pub-REK, address = pub-REK:adr, pages = "x + 343", year = "1968", ISBN = "0-88275-642-7", ISBN-13 = "978-0-88275-642-4", LCCN = "QA 297 C64 1978", bibdate = "Tue Dec 14 22:55:11 1993", note = "Reprinted 1978 with corrections.", acknowledgement = ack-nhfb, } @Book{Hart:1968:CAb, author = "John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall", title = "Computer Approximations", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "x + 343", year = "1968", ISBN = "0-471-35630-1", ISBN-13 = "978-0-471-35630-1", LCCN = "????", bibdate = "Sat Jan 14 14:53:06 2006", acknowledgement = ack-nhfb, } @Article{Nagashima:1968:EFN, author = "Takashi Nagashima", title = "On elementary functions of natural numbers", journal = "Hitotsubashi J. Arts Sci.", volume = "9", pages = "50--58", year = "1968", ISSN = "0073-2788", MRclass = "02.72", MRnumber = "MR0232678 (38 \#1001)", MRreviewer = "R. L. Goodstein", fjournal = "Hitotsubashi Journal of Arts \& Sciences", } @Article{Richardson:1968:SUP, author = "Daniel Richardson", title = "Some Undecidable Problems Involving Elementary Functions of a Real Variable", journal = j-J-SYMBOLIC-LOGIC, volume = "33", number = "4", pages = "514--520", month = dec, year = "1968", CODEN = "JSYLA6", ISSN = "0022-4812", MRclass = "02.75", MRnumber = "39 #1330", bibdate = "Mon May 19 13:04:20 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz", acknowledgement = ack-nhfb, } @Article{Wrench:1968:CTS, author = "John W. {Wrench, Jr.}", title = "Concerning Two Series for the Gamma Function", journal = j-MATH-COMPUT, volume = "22", number = "103", pages = "617--626", month = jul, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Carlson:1969:CBE, author = "B. C. Carlson", title = "A connection between elementary functions and higher transcendental functions", journal = j-SIAM-J-APPL-MATH, volume = "17", pages = "116--148", year = "1969", CODEN = "SMJMAP", ISSN = "0036-1399", MRclass = "33.20 (30.00)", MRnumber = "40 \#408", MRreviewer = "S. K. Bose", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Clark:1969:SCE, author = "N. W. Clark and W. J. Cody", title = "Self-contained exponentiation", crossref = "AFIPS:1969:ACPb", pages = "701--706", year = "1969", bibdate = "Wed Sep 07 10:49:33 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt, ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", acknowledgement = ack-nj, } @Article{Herman:1969:NHE, author = "G. T. Herman", title = "A new hierarchy of elementary functions", journal = j-PROC-AM-MATH-SOC, volume = "20", pages = "557--562", year = "1969", CODEN = "PAMYAR", ISSN = "0002-9939", MRclass = "02.77", MRnumber = "40 \#4110", MRreviewer = "G. E. Sacks", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Lewis:1969:FII, author = "Richard L. Lewis", title = "On Finite Integrals Involving Trigonometric, {Bessel}, and {Legendre} Functions", journal = j-MATH-COMPUT, volume = "23", number = "106", pages = "259--273", month = apr, year = "1969", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Tesler:1969:AEF, author = "G. S. Tesler", booktitle = "Mathematical provisioning of electronic digital computers and effective organization of the computing process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2", title = "The approximation of elementary functions by means of polynomials of degree zero and one. ({Russian})", publisher = "Akad. Nauk Ukrain. SSR", address = "Kiev, USSR", pages = "75--88", year = "1969", MRclass = "65D15", MRnumber = "45 \#4600", MRreviewer = "I. Selihova", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Turner:1969:DSC, author = "L. R. Turner", title = "Difficulty in {$\sin$\slash$\cos$} Routine", journal = j-SIGNUM, volume = "4", number = "3", pages = "13--13", year = "1969", CODEN = "SNEWD6", ISSN = "0163-5778", bibdate = "Thu Feb 15 15:23:23 2007", acknowledgement = ack-nhfb, } @Article{Zaker:1969:CCE, author = "T. A. Zaker", title = "Calculation of the complementary error function of complex argument", journal = j-J-COMPUT-PHYS, volume = "4", number = "3", pages = "427--430", month = oct, year = "1969", CODEN = "JCTPAH", DOI = "http://dx.doi.org/10.1016/0021-9991(69)90011-4", ISSN = "0021-9991", bibdate = "Thu Dec 04 16:20:39 2008", acknowledgement = ack-nhfb, } @TechReport{DeLugish:1970:CAA, author = "Bruce Gene DeLugish", title = "A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer", number = "399", institution = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, Illinois", pages = "191", year = "1970", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz", acknowledgement = ack-nhfb, } @Article{Kolbig:1970:CZI, author = "K. S. Kolbig", title = "Complex Zeros of an Incomplete {Riemann} Zeta Function and of the Incomplete Gamma Function", journal = j-MATH-COMPUT, volume = "24", number = "111", pages = "679--696", month = jul, year = "1970", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @TechReport{Lugish:1970:CAA, author = "B. G. de Lugish", title = "A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer", type = "Report", number = "399", institution = "Department of Computer Science, University of Illinois", pages = "????", month = jun, year = "1970", bibdate = "Fri Sep 02 22:49:20 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Ninomiya:1970:BRS, author = "Ichizo Ninomiya", title = "Best Rational Starting Approximations and Improved {Newton} Iteration for the Square Root", journal = j-MATH-COMPUT, volume = "24", number = "110", pages = "391--404", month = apr, year = "1970", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb # " and " # ack-nj, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Nagoya Univ., Chikua ku, Japan", keywords = "computing procedure; function approximation; iterative methods; Newton iteration; rational approximation; square root", treatment = "T Theoretical or Mathematical", } @TechReport{Rothmaier:1970:DSB, author = "B. Rothmaier", title = "{Dokumentation der Standardfunktionen des Betriebssystems {Hydra X8}} \toenglish {Documentation} of the Elementary Functions of the Operating System {Hydra X8} \endtoenglish", type = "Interner {Bericht}", number = "Nr. 70/8", institution = "Institut f{\"u}r Informatik, Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1970", bibdate = "Fri Jun 11 12:37:53 1999", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Bohan:1971:ADC, author = "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov", title = "The analytic definition of certain elementary functions. ({Russian}) Questions of modern mathematics and methods of teaching it at institutions of higher learning", journal = "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.", volume = "404", pages = "59--78", year = "1971", MRclass = "26A09", MRnumber = "55 \#10612", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Cody:1971:SEF, author = "W. J. Cody", title = "Software for the Elementary Functions", crossref = "Rice:1971:MS", pages = "171--186", year = "1971", bibdate = "Thu Sep 15 18:56:47 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Herman:1971:EDH, author = "G. T. Herman", title = "The equivalence of different hierarchies of elementary functions", journal = "Z. Math. Logik Grundlagen Math.", volume = "17", pages = "219--224", year = "1971", MRclass = "02.77 (68.00)", MRnumber = "44 \#6494", MRreviewer = "D. A. Clarke", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Kuki:1971:FEP, author = "H. Kuki and J. Ascoly", title = "{FORTRAN} extended-precision library", journal = j-IBM-SYS-J, volume = "10", number = "1", pages = "39--61", year = "1971", coden = "IBMSA7", ISSN = "0018-8670", bibdate = "Thu Sep 15 18:51:32 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt, ftp://ftp.math.utah.edu/pub/tex/bib/ibmsysj.bib, ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nj, xxmonth = "(none)", } @InCollection{Kuki:1971:MFS, author = "H. Kuki", title = "Mathematical Function Subprograms for Basic System Libraries{}\emdash Objectives, Constraints, and Trade-Off", crossref = "Rice:1971:MS", pages = "187--199", year = "1971", bibdate = "Fri Sep 16 16:27:40 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nj, } @Article{Liron:1971:ISR, author = "N. Liron", title = "Infinite Sums of Roots for a Class of Transcendental Equations and {Bessel} Functions of Order One-Half", journal = j-MATH-COMPUT, volume = "25", number = "116", pages = "769--781", month = oct, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Luke:1971:MTBa, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "323--330", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Luke:1971:MTBb, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions, {II}", journal = j-MATH-COMPUT, volume = "25", number = "116", pages = "789--795", month = oct, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Matta:1971:UCE, author = "F. Matta and A. Reichel", title = "Uniform Computation of the Error Function and Other Related Functions", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "339--344", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @PhdThesis{Rothmaier:1971:BEF, author = "B. Rothmaier", title = "{Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit} \toenglish {The Computation of Elementary Functions with Arbitrary Accuracy} \endtoenglish", type = "Dissertation", school = "Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1971", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Spellucci:1971:DPA, author = "P. Spellucci", title = "Double precision approximations to the elementary functions using {Jacobi-fractions}", journal = j-NUM-MATH, volume = "18", pages = "127--143", year = "1971/1972", CODEN = "NUMMA7", ISSN = "0029-599X", MRclass = "65D20", MRnumber = "45 \#7938", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Spira:1971:CGF, author = "Robert Spira", title = "Calculation of the Gamma Function by {Stirling}'s Formula", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "317--322", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Walther:1971:UAE, author = "J. S. Walther", title = "A unified algorithm for elementary functions", crossref = "AFIPS:1971:ACP", volume = "38", pages = "379--385", year = "1971", bibdate = "Thu Sep 1 10:15:31 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Book{Bark:1972:MTF, author = "L. S. Bark", title = "{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh funktsi{\u{\i}}} (${\rm sin} x$, ${\rm cos} x$, $e^{x}$ {\cyr i} $e^{-x}$). ({Russian}) [Multiplace tables of the elementary functions (${\rm sin}\ x$, ${\rm cos}\ x$, $e^{x}$ and $e^{-x}$)]", publisher = "Vy{\v{c}}isl. Centr Akad. Nauk SSSR", address = "Moscow, USSR", edition = "Second, unrevised", pages = "134", year = "1972", MRclass = "65A05", MRnumber = "50 \#6100", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "Tables processed and text translated from the English by L. S. Bark. Library of Mathematical Tables, No. 9. 1972", acknowledgement = ack-nhfb, } @Article{Carlson:1972:ACL, author = "B. C. Carlson", title = "An algorithm for computing logarithms and arctangents", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "543--549", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Iowa State Univ., Ames, IA, USA", keywords = "acceleration; arctangents; auxiliary; Borchardt's algorithm; convergence; fast; function approximation; functions; inverse circular functions; inverse hyperbolic; iterative algorithm; logarithms; numerical methods; rational operations; recurrence relation; square roots", treatment = "T Theoretical or Mathematical", } @Article{Chen:1972:ACE, author = "Tien Chi Chen", title = "Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots", journal = j-IBM-JRD, volume = "16", number = "4", pages = "380--388", month = jul, year = "1972", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65D20", MRnumber = "49 \#1738", bibdate = "Tue Mar 25 14:26:59 MST 1997", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf", abstract = "It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $(x, y)$ such that the $F(x, y) = f(x_0)$ is invariant; when $x$ is driven towards a known value $x_w$, $y$ is driven towards the result. For an $N$-bit fraction about $N / 4$ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.", acknowledgement = ack-nhfb # " and " # ack-nj, classcodes = "C5230 (Digital arithmetic methods)", corpsource = "IBM, San Jose, CA, USA", keywords = "adds; APL; bit counting; convergence; cotransformation; digital arithmetic; errors; exponentials; high speed table; iteration; logarithms; lookups; ratios; shifts; simulation; square roots; termination algorithm", reviewer = "F. Gotze", treatment = "P Practical", } @TechReport{Ercegovac:1972:RES, author = "Milos D. Ercegovac", title = "Radix 16 Evaluation of Some Elementary Functions", number = "540", institution = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, Illinois", pages = "30", year = "1972", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz", acknowledgement = ack-nhfb, } @Article{Hunter:1972:NEC, author = "D. B. Hunter and T. Regan", title = "A note on the evaluation of the complementary error function", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "539--541", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Univ. Bradford, UK", keywords = "complementary error function; complex variable; evaluation; integration; method of Matta and Reichel; modification; numerical; stability", treatment = "T Theoretical or Mathematical", } @Article{Kolbig:1972:ZIG, author = "K. S. Kolbig", title = "On the Zeros of the Incomplete Gamma Function", journal = j-MATH-COMPUT, volume = "26", number = "119", pages = "751--755", month = jul, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "CERN, Geneva, Switzerland", keywords = "asymptotic formulae; complex w plane; function approximation; incomplete gamma function; poles and zeros; zeros", treatment = "T Theoretical or Mathematical", } @Article{Ling:1972:EM, author = "Chih-Bing Ling and Jung Lin", title = "On Evaluation of Moments of ${K}_\nu(t)/{I}_\nu(t)$", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "529--537", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4190 (Other numerical methods)", corpsource = "Virginia Politech. Inst., Blacksburg, VA, USA", keywords = "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t); numerical methods; Watson's method", treatment = "T Theoretical or Mathematical", } @Article{Linz:1972:MCB, author = "Peter Linz", title = "A Method for Computing {Bessel} Function Integrals", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "509--513", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Univ. California, Davis, CA, USA", keywords = "Abel; Bessel function integrals; Fourier integrals; infinite integrals; integration; numerical computation; transform", treatment = "T Theoretical or Mathematical", } @Article{Luke:1972:MTB, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions. {III}", journal = j-MATH-COMPUT, volume = "26", number = "117", pages = "237--240", month = jan, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4190 (Other numerical methods)", corpsource = "Univ. Missouri, Kansas City, KS, USA", keywords = "Bessel functions; miniaturized tables; numerical methods", treatment = "T Theoretical or Mathematical", } @Article{MacKinnon:1972:AEH, author = "Robert F. MacKinnon", title = "The asymptotic expansions of {Hankel} transforms and related integrals", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "515--527", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0230 (Integral transforms); C1130 (Integral transforms)", corpsource = "Defence Res. Establ., Pacific, Victoria, BC, Canada", keywords = "asymptotic expansions; Bessel; functions; Hankel transforms; integrals; transforms", treatment = "T Theoretical or Mathematical", } @TechReport{Manos:1972:CCA, author = "Paul Manos and L. Richard Turner", title = "Constrained {Chebyshev} approximations to some elementary functions suitable for evaluation with floating-point arithmetic", type = "{NASA} Technical Note", number = "TN D-6698", institution = "NASA", address = "Washington, DC, USA", pages = "iii + 68", month = mar, year = "1972", bibdate = "Mon May 22 11:27:24 2006", URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf", acknowledgement = ack-nhfb, } @Article{Marino:1972:NAA, author = "D. Marino", title = "New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions", journal = j-IEEE-TRANS-COMPUT, volume = "21", number = "12", pages = "1416--1421", month = dec, year = "1972", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Sep 08 08:05:51 1994", acknowledgement = ack-nj, } @Article{Olver:1972:NBR, author = "F. W. J. Olver and D. J. Sookne", title = "Note on Backward Recurrence Algorithms", journal = j-MATH-COMPUT, volume = "26", number = "120", pages = "941--947", month = oct, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290Z (Other numerical methods); C4190 (Other numerical methods)", corpsource = "Univ. Maryland, College Park, MD, USA", keywords = "backward recurrence algorithms; Bessel; Bessel functions; difference equations; functions; recessive solution; second order linear difference equation", treatment = "T Theoretical or Mathematical", } @Article{Parnes:1972:CZM, author = "R. Parnes", title = "Complex zeros of the modified {Bessel} function {$K_n(Z)$}", journal = j-MATH-COMPUT, volume = "26", number = "120", pages = "949--953", month = oct, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "City Univ., New York, NY, USA", keywords = "and zeros; Bessel functions; complex zeros; interpolation; interpolation scheme; iterative; iterative methods; modified Bessel function; poles", treatment = "T Theoretical or Mathematical", } @Article{Turunov:1972:EFD, author = "M. Turunov", title = "Elementary functions of a discrete real and complex argument. ({Russian})", journal = "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy", volume = "418 Voprosy Mat.", pages = "263--271, 386", year = "1972", MRclass = "30A95", MRnumber = "50 \#13556", MRreviewer = "G. Berzsenyi", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Baker:1973:PAS, author = "P. W. Baker", title = "Predictive algorithms for some elementary functions in radix $2$", journal = j-ELECT-LETTERS, volume = "9", pages = "493--494", year = "1973", CODEN = "ELLEAK", ISBN = "0013-5194", ISBN-13 = "0013-5194", ISSN = "0013-5194", MRclass = "68A10", MRnumber = "57 \#18203", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Cody:1973:CAP, author = "W. J. Cody and Anthony J. Strecok and Henry C. {Thacher, Jr.}", title = "{Chebyshev} Approximations for the Psi Function", journal = j-MATH-COMPUT, volume = "27", number = "121", pages = "123--127", month = jan, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65-06 (68-06)", MRnumber = "50 6095", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Argonne Nat. Lab., IL, USA", keywords = "Chebyshev approximation; Chebyshev approximations; digamma function; psi function", treatment = "T Theoretical or Mathematical", } @Article{Ercegovac:1973:REC, author = "M. D. Ercegovac", title = "Radix-16 Evaluation of Certain Elementary Functions", journal = j-IEEE-TRANS-COMPUT, volume = "C-22", number = "6", pages = "561--566", month = jun, year = "1973", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Sep 1 10:15:39 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Fettis:1973:CZE, author = "Henry E. Fettis and James C. Caslin and Kenneth R. Cramer", title = "Complex zeros of the error function and of the complementary error function", journal = j-MATH-COMPUT, volume = "27", number = "122", pages = "401--407", month = apr, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Wright-Patterson Air Force Base, OH, USA", keywords = "asymptotic formula; complementary error function; complex zeros; error function; errors; first one hundred zeros; function evaluation; poles and zeros", treatment = "T Theoretical or Mathematical", } @Article{Fettis:1973:SPC, author = "Henry E. Fettis and James C. Caslin and Kenneth R. Cramer", title = "Saddle Points of the Complementary Error Function", journal = j-MATH-COMPUT, volume = "27", number = "122", pages = "409--412", month = apr, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Sandia Labs., Albuquerque, NM, USA", keywords = "asymptotic; complementary error function; errors; formula; function evaluation; poles and zeros; saddle points", treatment = "T Theoretical or Mathematical", } @TechReport{Hemker:1973:SDL, author = "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen} and H. L. Oudshoorn and D. T. Winter", title = "Single- and double-length computation of elementary functions", number = "NW 7", institution = "Mathematical Centre", address = "Amsterdam", year = "1973", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib", acknowledgement = ack-nhfb, } @Article{Linz:1973:NCI, author = "Peter Linz and T. E. Kropp", title = "A note on the computation of integrals involving products of trigonometric and {Bessel} functions", journal = j-MATH-COMPUT, volume = "27", number = "124", pages = "871--872", month = oct, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Univ. California, Davies, CA, USA", keywords = "Bessel functions; computation; integration; numerical; numerical methods; products; trigonometric", treatment = "T Theoretical or Mathematical", } @Article{Lozier:1973:BCP, author = "D. W. Lozier and L. C. Maximon and W. L. Sadowski", title = "A bit comparison program for algorithm testing", journal = j-COMP-J, volume = "16", number = "2", pages = "111--117", month = may, year = "1973", CODEN = "CMPJA6", ISSN = "0010-4620", bibdate = "Fri Sep 29 08:52:11 MDT 2000", bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif", acknowledgement = ack-nhfb, classcodes = "C6150G (Diagnostic, testing, debugging and evaluating systems)", corpsource = "Nat. Bur. Stand., Washington, DC, USA", keywords = "accuracy; algorithm testing; bit comparison program; computer algorithms; program debugging", treatment = "P Practical", } @Article{McNolty:1973:SPD, author = "Frank McNolty", title = "Some probability density functions and their characteristic functions", journal = j-MATH-COMPUT, volume = "27", number = "123", pages = "495--504", month = jul, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0240 (Probability and statistics); C1140 (Probability and statistics)", corpsource = "Lockheed Palo Alto Res. Lab., CA, USA", keywords = "Bessel function; characteristic functions; functions; hypergeometric function; probability; probability density functions", treatment = "T Theoretical or Mathematical", } @Article{Amos:1974:CMB, author = "D. E. Amos", title = "Computation of modified {Bessel} functions and their ratios", journal = j-MATH-COMPUT, volume = "28", number = "125", pages = "239--251", month = jan, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Sandia Labs., Albuquerque, NM, USA", keywords = "Bessel functions; computation; low order Bessel functions; modified Bessel functions; monotonicity; properties; ratios; recursion; relation", treatment = "T Theoretical or Mathematical", } @Article{Blair:1974:RCA, author = "J. M. Blair", title = "Rational {Chebyshev} approximations for the modified {Bessel} functions {$I_0(x)$} and {$I_1(x)$}", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "581--583", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy Canada Ltd., Chalk River, Ont., Canada", keywords = "Chebyshev approximation; functions; modified Bessel; nearly best rational approximations; rational Chebyshev approximations; series (mathematics)", treatment = "T Theoretical or Mathematical", } @Article{Buschman:1974:FSR, author = "R. G. Buschman", title = "Finite sum representations for partial derivatives of special functions with respect to parameters", journal = j-MATH-COMPUT, volume = "28", number = "127", pages = "817--824", month = jul, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Univ. Wyoming, Laramie, WY, USA", keywords = "Bessel functions; differentiation; finite sum representations; finite sums; functions; G function; Gegenbauer functions; hypergeometric; Legendre; Mellin transformation; partial derivatives; special functions; Whittaker functions", treatment = "T Theoretical or Mathematical", } @Article{Fettis:1974:SAC, author = "Henry E. Fettis", title = "A stable algorithm for computing the inverse error function in the `tail-end' region", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "585--587", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Wright-Patterson Air Force Base, OH, USA", keywords = "function evaluation; inverse error function; iterative algorithm; stability; stable algorithm; tail end region", treatment = "T Theoretical or Mathematical", } @Article{Glasser:1974:SDI, author = "M. L. Glasser", title = "Some definite integrals of the product of two {Bessel} functions of the second kind: (order zero)", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "613--615", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Battelle Memorial Inst., Columbus, OH, USA", keywords = "Bessel functions; definite integrals; evaluate; function evaluation; integral representation; order; second kind; zero", treatment = "T Theoretical or Mathematical", } @Article{Nasell:1974:IMB, author = "Ingemar Nasell", title = "Inequalities for Modified {Bessel} Functions", journal = j-MATH-COMPUT, volume = "28", number = "125", pages = "253--256", month = jan, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Bell Labs., Holmdel, NJ, USA", keywords = "Bessel functions; inequalities; modified Bessel functions; sharp versions", treatment = "T Theoretical or Mathematical", } @Article{Pisarskii:1974:QCD, author = "A. V. Pisarski{{\u{\i}}} and A. F. Kurgaev and A. V. Palagin", title = "On the question of the convergence of the {``digit by digit''} methods of computing the elementary functions", journal = "Kibernetika (Kiev)", volume = "4", pages = "147--149", year = "1974", CODEN = "KBRNA5", ISSN = "0023-1274", MRclass = "65D20", MRnumber = "53 \#1915", MRreviewer = "V. V. Ivanov", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Wang:1974:UEZ, author = "Paul S. Wang", title = "The Undecidability of the Existence of Zeros of Real Elementary Functions", journal = j-J-ACM, volume = "21", number = "4", pages = "586--589", month = oct, year = "1974", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database, ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib", abstract = "From Richardson's undecidability results, it is shown that the predicate ``there exists a real number such that G(r) equals 0'' is recursively undecidable for G(x) in a class of functions which involves polynomials and the sine function. The deduction follows that the convergence of a class of improper integrals is recursively undecidable.", acknowledgement = ack-nhfb, classification = "921", journalabr = "J Assoc Comput Mach", keywords = "mathematical techniques", } @Article{Baker:1975:MER, author = "P. W. Baker", title = "More efficient radix-$2$ algorithms for some elementary functions", journal = j-IEEE-TRANS-COMPUT, volume = "C-24", number = "11", pages = "1049--1054", month = nov, year = "1975", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "68A10", MRnumber = "52 \#7193", MRreviewer = "I. Kaufmann", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb, } @TechReport{Brent:1975:MZM, author = "R. P. (Richard P.) Brent", title = "Multiple-precision zero-finding methods and the complexity of elementary function evaluation", institution = "Department of Computer Science, Carnegie-Mellon University", address = "Pittsburgh, PA, USA", pages = "26", year = "1975", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, keywords = "Iterative methods (Mathematics)", searchkey = "ti:elementary n1 function", } @Article{Carta:1975:LOA, author = "David G. Carta", title = "Low-Order Approximations for the Normal Probability Integral and the Error Function", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "856--862", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0260 (Optimisation techniques); B0290R (Integral equations); C1180 (Optimisation techniques); C4180 (Integral equations)", corpsource = "Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA", keywords = "error function; fraction; integral equations; linear minimax problems; linear programming; low; normal probability integral; order approximations; polynomials; rational", treatment = "T Theoretical or Mathematical", } @PhdThesis{Epstein:1975:AET, author = "Harvey Irwin Epstein", title = "Algorithms for elementary transcendental function arithmetic", school = "University of Wisconsin", address = "Madison, WI, USA", pages = "409", year = "1975", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, annote = "Typescript. Vita. Thesis (Ph. D.)--University of Wisconsin--Madison, 1975.", keywords = "Functions, Transcendental.; Algorithms.; Functions -- Data processing.", searchkey = "ti:elementary n1 function", } @Article{Headley:1975:DZG, author = "V. B. Headley and V. K. Barwell", title = "On the distribution of the zeros of generalized {Airy} functions", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "863--877", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290P (Differential equations); C4170 (Differential equations)", corpsource = "Dept. of Math., Brock Univ., St. Catherines, Ont., Canada", keywords = "Bessel functions; boundary rays; differential equations; generalized Airy functions; nonreal zeros; zeros distribution", treatment = "T Theoretical or Mathematical", } @InProceedings{Hitotumatu:1975:SRU, author = "Sin Hitotumatu", title = "Some remarks on the unified treatment of elementary functions by microprogramming", crossref = "Miller:1975:TNA", pages = "51--56 (vol. 2)", year = "1975", MRclass = "65D15", MRnumber = "54 \#11733", MRreviewer = "Luciano Biasini", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Ikebe:1975:ZRC, author = "Yasuhiko Ikebe", title = "The Zeros of Regular {Coulomb} Wave Functions and of Their Derivatives", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "878--887", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Centre Numerical Analysis, Univ. of Texas, Austin, TX, USA", keywords = "Bessel function; compact matrix; eigenvalues; eigenvalues and eigenfunctions; function zeros characterisation; matrix algebra; methods; numerical; operators; regular Coulomb wave functions; wave functions; zeros", treatment = "T Theoretical or Mathematical", } @Article{Ng:1975:CCM, author = "Edward W. Ng", title = "A Comparison of Computational Methods and Algorithms for the Complex Gamma Function", journal = j-TOMS, volume = "1", number = "1", pages = "56--70", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/355626.355635", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "52 #2148", bibdate = "Fri Aug 26 23:44:16 1994", acknowledgement = ack-nhfb, reviewer = "R. H. Bartels", } @Article{Temme:1975:UAE, author = "N. M. Temme", title = "Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function", journal = j-MATH-COMPUT, volume = "29", number = "132", pages = "1109--1114", month = oct, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Appl. Math., Amsterdam, Netherlands", keywords = "asymptotic expansions; asymptotic series; complementary error function; function approximation; incomplete beta function; incomplete gamma functions; uniform", treatment = "T Theoretical or Mathematical", } @TechReport{Warner:1975:PDG, author = "D. D. Warner", title = "A partial derivative generator", type = "Computing Science Technical Report", number = "28", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", year = "1975", bibdate = "Mon May 19 13:30:58 1997", bibsource = "Theory/auto.diff.bib", abstract = "A precompiler is described which takes a specification of a function as input and produces a Fortran subroutine which will evaluate the component functions and the corresponding Jacobian. Many of the Fortran elementary functions are provided, as well as a facility which allows the user to specify their own differentiation rules.", acknowledgement = ack-nhfb, keywords = "differentiation arithmetic; precompiler.", referred = "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].", } @Article{Blair:1976:RCA, author = "J. M. Blair and C. A. Edwards and J. H. Johnson", title = "Rational {Chebyshev} approximations for the inverse of the error function", journal = j-MATH-COMPUT, volume = "30", number = "136", pages = "827--830", month = oct, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy of Canada Ltd., Chalk River Nuclear Lab., Chalk River, Ont., Canada", keywords = "Chebyshev approximation; Chebyshev approximations; error function; inverse; rational", treatment = "T Theoretical or Mathematical", } @Article{Brent:1976:FMP, author = "Richard P. Brent", title = "Fast Multiple-Precision Evaluation of Elementary Functions", journal = j-J-ACM, volume = "23", number = "2", pages = "242--251", month = apr, year = "1976", CODEN = "JACOAH", DOI = "http://doi.acm.org/10.1145/321941.321944", ISSN = "0004-5411", MRclass = "68A20 (68A10)", MRnumber = "52 \#16111", MRreviewer = "Amnon Barak", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", abstract = "Let $f(x)$ be one of the usual elementary functions ($\exp$, $\log$, $\artan$, $\sin$, $\cosh$, etc.), and let $M(n)$ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $f(x)$ can be evaluated, with relative error $O(2-n)$, in $O(M(n)log (n))$ operations as $n \rightarrow \infty$, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Sch{\"o}nhage--Strassen bound on $M(n)$, it follows that an $n$-bit approximation to $f(x)$ may be evaluated in $O(n \log_(n) \log \log(n))$ operations. Special cases include the evaluation of constants such as $\pi$ $e$, and $e^\pi$. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.", acknowledgement = ack-nhfb, classification = "723", journalabr = "J Assoc Comput Mach", keywords = "computational complexity; computer arithmetic; computer programming", } @InProceedings{Brent:1976:MPZ, author = "Richard P. Brent", title = "Multiple-precision zero-finding methods and the complexity of elementary function evaluation", crossref = "Traub:1976:ACC", pages = "151--176", year = "1976", MRclass = "68A20", MRnumber = "54 \#11843", MRreviewer = "Claus-Peter Schnorr", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Buschman:1976:IHF, author = "R. G. Buschman", title = "Inequalities for Hypergeometric Functions", journal = j-MATH-COMPUT, volume = "30", number = "134", pages = "303--305", month = apr, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", corpsource = "Dept. of Math. and Statistics, Univ. of Guelph, Guelph, Ont., Canada", keywords = "Bessel functions; classical orthogonal polynomials; confluence; dominant diagonal matrix; function; functions; Gauss' hypergeometric; hypergeometric functions; Kummer's hypergeometric function; modified Bessel function; principle", treatment = "T Theoretical or Mathematical", } @Article{Ellacott:1976:RCA, author = "S. Ellacott and Jack Williams", title = "Rational {Chebyshev} Approximation in the Complex Plane", journal = j-SIAM-J-NUMER-ANAL, volume = "13", number = "3", pages = "310--323", month = jun, year = "1976", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Fettis:1976:CR, author = "Henry E. Fettis", title = "Complex Roots of $\sin z = az, \cos z = az$, and $\cosh z = az$", journal = j-MATH-COMPUT, volume = "30", number = "135", pages = "541--545", month = jul, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", keywords = "complex roots; cos z=az; cosh z=az; functional equations; sin z=az", treatment = "T Theoretical or Mathematical", } @Article{Kononova:1976:CEF, author = "N. F. Kononova", title = "The computation of elementary functions by means of polynomial approximations by the method of {V. K. Dzjadik}. ({Russian})", journal = "Vy{\v{c}}isl. Prikl. Mat. (Kiev)", volume = "29", pages = "27--39", year = "1976", ISSN = "0321-4117", MRclass = "151. 65D15", MRnumber = "57 \#18026", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Paul:1976:SEF, author = "George Paul and M. Wayne Wilson", title = "Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?", journal = j-TOMS, volume = "2", number = "2", pages = "132--142", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", acknowledgement = ack-nhfb, } @InCollection{Salimov:1976:OCE, author = "F. I. Salimov", booktitle = "Probabilistic methods and cybernetics", title = "The organization of calculations of elementary functions into tables. ({Russian})", volume = "12--13", publisher = "Kazan. Univ.,", address = "Kazan, USSR", pages = "77--90", year = "1976", MRclass = "65A05", MRnumber = "58 \#31706", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Siemieniuch:1976:PCR, author = "J. L. Siemieniuch", title = "Properties of certain rational approximations to $e^{-z}$", journal = j-BIT, volume = "16", number = "2", pages = "172--191", month = jun, year = "1976", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931369", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:14 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172", acknowledgement = ack-nhfb, keywords = "elefunt; elementary functions", } @Article{Danilcenko:1977:ETC, author = "L. S. Danil'{\v{c}}enko", title = "An efficient technique for the construction of rational approximations of elementary functions. ({Russian}) Optimization of computations (approximation and minimization of functions)", journal = "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint", volume = "18", pages = "17--21", year = "1977", MRclass = "65D15", MRnumber = "80b:65016", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Dzjadyk:1977:TPA, author = "V. K. Dzjadyk and S. F. Karpenko", title = "Tables of polynomials for the approximate solution of elementary functions. ({Russian})", number = "28", institution = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint", pages = "28", year = "1977", MRclass = "65A05 (65D20)", MRnumber = "58 \#19016", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Dzyadyk:1977:OPM, author = "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko and N. F. Kononova", title = "{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami {\`e}lementarnykh funktsi{\u{\i}}.} ({Russian}) [Efficient approximation by polynomials of elementary functions]", type = "Preprint", number = "IM-77-21", institution = "Akad. Nauk Ukrain. SSR Inst. Mat.", address = "Kiev, USSR", pages = "42", year = "1977", MRclass = "65L99", MRnumber = "57 \#11075", MRreviewer = "B. D. Donevski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Gautschi:1977:ACC, author = "Walter Gautschi", title = "Anomalous convergence of a continued fraction for ratios of {Kummer} functions", journal = j-MATH-COMPUT, volume = "31", number = "140", pages = "994--999", month = oct, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis); C4170 (Differential equations)", corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA", keywords = "apparent; Bessel functions; continued fraction; convergence; differential equations; gamma functions; Kummer functions; wrong limit", treatment = "T Theoretical or Mathematical", } @Article{McCarthy:1977:OAE, author = "D. P. McCarthy", title = "The optimal algorithm to evaluate $x^n$ using elementary multiplication methods", journal = j-MATH-COMP, volume = "31", number = "137", pages = "251--256", month = jan, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4120 (Functional analysis); C4240 (Programming and algorithm theory)", keywords = "computational complexity; function evaluation; optimal multiplication chains; symbolic algebraic manipulation", treatment = "T Theoretical or Mathematical", } @Article{Pexton:1977:RTTa, author = "Robert L. Pexton and Arno D. Steiger", title = "Roots of two transcendental equations involving spherical {Bessel} functions", journal = j-MATH-COMPUT, volume = "31", number = "139", pages = "752--753", month = jul, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra)", corpsource = "Univ. of California, Livermore, CA, USA", keywords = "Bessel functions; root; spherical Bessel functions; transcendental equations", treatment = "T Theoretical or Mathematical", } @Article{Andrews:1978:UEF, author = "M. Andrews and T. Mraz", title = "Unified elementary function generator", journal = j-MICROPROC-MICROSYS, volume = "2", number = "5", pages = "270--273", month = oct, year = "1978", CODEN = "MIMID5", ISSN = "0141-9331", bibdate = "Thu Sep 1 10:15:39 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Benton:1978:CZT, author = "T. C. Benton and H. D. Knoble", title = "Common Zeros of Two {Bessel} Functions", journal = j-MATH-COMPUT, volume = "32", number = "142", pages = "533--535", month = apr, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra)", corpsource = "Pennsylvania State Univ., University Park, PA, USA", keywords = "Bessel functions; common zeros; poles and zeros; positive zeros; zeros", treatment = "T Theoretical or Mathematical", } @Article{Blair:1978:RCA, author = "J. M. Blair and C. A. Edwards and J. H. Johnson", title = "Rational {Chebyshev} approximations for the {Bickley} functions {$Ki_n(x)$}", journal = j-MATH-COMPUT, volume = "32", number = "143", pages = "876--886", month = jul, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy of Canada Ltd., Chalk River, Ont., Canada", keywords = "approximation; Bessel functions; Bickley functions; Chebyshev approximation; Chebyshev approximations; function; recurrence; relation", treatment = "T Theoretical or Mathematical", } @Article{Chin:1978:DAD, author = "R. C. Y. Chin and G. W. Hedstrom", title = "A dispersion analysis for difference schemes: tables of generalized {Airy} functions", journal = j-MATH-COMPUT, volume = "32", number = "144", pages = "1163--1170", month = oct, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation); C4170 (Differential equations)", corpsource = "Univ. of California, Lawrence Livermore Lab., Livermore, CA, USA", keywords = "artificial viscosity; difference schemes; dispersion analysis; function approximation; functions; generalized Airy; linear hyperbolic equation", treatment = "T Theoretical or Mathematical", } @Article{DiDonato:1978:AR, author = "A. R. DiDonato", title = "An Approximation for $\int^\infty_x e^{-t^2/2} t^p dt, x > 0, p$ Real", journal = j-MATH-COMPUT, volume = "32", number = "141", pages = "271--275", month = jan, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Naval Surface Weapons Center, Dahlgren, VA, USA", keywords = "integral approximation; integration; numerical analysis", treatment = "A Application; N New Development; T Theoretical or Mathematical", } @Article{Dzjadyk:1978:CRP, author = "V. K. Dzjadyk and L. \=I. F{\'\i}lozof", title = "The convergence rate of Pad{\'e} approximants for some elementary functions. ({Russian})", journal = "Mat. Sb. (N.S.)", volume = "107(149)", number = "3", pages = "347--363, 463", year = "1978", ISSN = "0368-8666", MRclass = "41A21 (30E10 41A25)", MRnumber = "81b:41043", MRreviewer = "B. D. Donevski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Frankowski:1978:RME, author = "Krzysztof S. Frankowski", title = "A Realistic Model for Error Estimates in the Evaluation of Elementary Functions", crossref = "IEEE:1978:PSC", pages = "70--74", year = "1978", MRclass = "65G05 (65D20)", MRnumber = "80g:65050", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb, } @Article{Gautschi:1978:CMB, author = "Walter Gautschi and Josef Slavik", title = "On the computation of modified {Bessel} function ratios", journal = j-MATH-COMPUT, volume = "32", number = "143", pages = "865--875", month = jul, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA", keywords = "Bessel; Bessel functions; continued fraction; fraction; function approximation; functions; Gauss' continued; modified Bessel function ratios; Perron's continued fraction", treatment = "T Theoretical or Mathematical", } @InProceedings{Hull:1978:DFP, author = "T. E. Hull", title = "Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation", crossref = "IEEE:1978:PSC", pages = "63--69", year = "1978", bibdate = "Thu Sep 01 12:14:34 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Pexton:1978:RTT, author = "Robert L. Pexton and Arno D. Steiger", title = "Roots of two transcendental equations as functions of a continuous real parameter", journal = j-MATH-COMPUT, volume = "32", number = "142", pages = "511--518", month = apr, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra)", corpsource = "Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA", keywords = "continuous real parameter; equations; roots; spherical Bessel functions; transcendental equations", treatment = "T Theoretical or Mathematical", } @Article{Schmidt:1978:EI, author = "Paul W. Schmidt", title = "Evaluation of the Integral $\int^\infty_0 \frac{t^{2\alpha-1} J_\nu(x\sqrt{1 + t^2})}{(1 + t^2)^{\alpha+\beta-1}} dt$", journal = j-MATH-COMPUT, volume = "32", number = "141", pages = "265--269", month = jan, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Phys. Dept., Univ. of Missouri, Columbia, MO, USA", keywords = "cylinder diameter distribution; first kind Bessel function; integral evaluation; integration; long circular; neutron scattering data; numerical analysis; power series expansions; recurrence; relations", treatment = "A Application; T Theoretical or Mathematical", } @Article{Schonfelder:1978:CEE, author = "J. L. Schonfelder", title = "{Chebyshev} expansions for the error and related functions", journal = j-MATH-COMPUT, volume = "32", number = "144", pages = "1232--1240", month = oct, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)", corpsource = "Computer Centre, Univ. of Birmingham, Birmingham, UK", keywords = "approximations; Chebyshev approximation; Chebyshev expansions; error analysis; error function; mappings; NAG library", treatment = "T Theoretical or Mathematical", } @Article{Atkins:1979:FSC, author = "D. E. Atkins", title = "{Fourth Symposium on Computer Arithmetic}: crunching with quality and {LSI}", journal = j-COMPUTER, volume = "12", number = "4", pages = "94--97", month = apr, year = "1979", CODEN = "CPTRB4", ISSN = "0018-9162", bibdate = "Thu Dec 12 07:20:54 MST 1996", bibsource = "Compendex database", abstract = "Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.", acknowledgement = ack-nhfb, classification = "722; 723", journalabr = "Computer", keywords = "computer arithmetic; computer systems, digital; data processing --- data description; mathematical techniques --- digital arithmetic", } @Article{Babb:1979:OEC, author = "Stanley E. {Babb, Jr.} and James W. Cafky", title = "Operational evaluation of certain infinite {Bessel} function integrals", journal = j-MATH-COMPUT, volume = "33", number = "147", pages = "1033--1039", month = jul, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "44A99", MRnumber = "80e:44002", MRreviewer = "L. Arteaga", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4180 (Integral equations)", corpsource = "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman, OK, USA", keywords = "Bessel function integral; integration; numerical methods; Schafheitlin method; trigonometric function; Weber", treatment = "A Application; T Theoretical or Mathematical", } @Article{Conde:1979:Z, author = "S. Conde and S. L. Kalla", title = "The $\nu $-zeros of ${J}_{-\nu }(x)$", journal = j-MATH-COMPUT, volume = "33", number = "145", pages = "423--426", month = jan, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20", MRnumber = "80b:65021", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4170 (Differential equations); C4190 (Other numerical methods)", corpsource = "Facultad de Ingenieria, Univ. del Zulia, Maracaibo, Venezuela", keywords = "Bessel function; boundary value; boundary-value problems; J/sub -v/(x); partial differential equations; poles and zeros; problems; transforms; v-zeros", treatment = "T Theoretical or Mathematical", } @Article{Epstein:1979:STE, author = "H. I. Epstein and B. F. Caviness", title = "A structure theorem for the elementary functions and its application to the identity problem", journal = j-INT-J-COMPUT-INF-SCI, volume = "8", number = "1", pages = "9--37", year = "1979", CODEN = "IJCIAH", ISSN = "0091-7036", MRclass = "12H05 (68C05)", MRnumber = "80k:12032", MRreviewer = "Michael F. Singer", bibdate = "Sat Apr 26 12:45:53 1997", acknowledgement = ack-nhfb, } @Article{Fettis:1979:AEU, author = "Henry E. Fettis", title = "An asymptotic expansion for the upper percentage points of the $\chi^{2}$-distribution", journal = j-MATH-COMPUT, volume = "33", number = "147", pages = "1059--1064", month = jul, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "62E20", MRnumber = "80h:62014", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", keywords = "approximation theory; asymptotic expansion; upper percentage point", treatment = "A Application; T Theoretical or Mathematical", } @Article{Gabutti:1979:HPM, author = "Bruno Gabutti", title = "On high precision methods for computing integrals involving {Bessel} functions", journal = j-MATH-COMPUT, volume = "33", number = "147", pages = "1049--1057", month = jul, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D30", MRnumber = "80c:65048", MRreviewer = "K. Jetter", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4180 (Integral equations); C4240 (Programming and algorithm theory)", corpsource = "Istituto di Calcoli Numerici, Univ. di Torino, Torino, Italy", keywords = "Bessel function integral; computational complexity; exponential function integral; integration", treatment = "T Theoretical or Mathematical", } @Article{Glasser:1979:NI, author = "M. L. Glasser", title = "A Note on the Integral $\int^\infty_0t^{2\alpha-1}(1 + t^2)^{1-\alpha-\beta} {J}_\nu(x\sqrt{1 + t^2}) dt$", journal = j-MATH-COMPUT, volume = "33", number = "146", pages = "792--793", month = apr, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40", MRnumber = "80d:33004", MRreviewer = "T. Erber", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis); C4180 (Integral equations)", corpsource = "Math. and Computer Sci. Dept., Clarkson Coll. of Technol., Potsdam, NY, USA", keywords = "Bessel functions; hypergeometric series; integral; integral equations", treatment = "T Theoretical or Mathematical", } @Article{Johnson:1979:RAF, author = "Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall", title = "Reducibility Among Floating-Point Graphs", journal = j-J-ACM, volume = "26", number = "4", pages = "739--760", month = oct, year = "1979", CODEN = "JACOAH", ISSN = "0004-5411", MRclass = "65G05", MRnumber = "80i:65045", bibdate = "Fri Dec 08 11:55:10 1995", abstract = "The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.", acknowledgement = ack-nhfb, } @Article{Leung:1979:AFE, author = "K. V. Leung and S. S. Ghaderpanah", title = "An application of the finite element approximation method to find the complex zeros of the modified {Bessel} function ${K}_{n}(z)$", journal = j-MATH-COMPUT, volume = "33", number = "148", pages = "1299--1306", month = oct, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (33-04)", MRnumber = "80e:65024", MRreviewer = "R. P. Boas, Jr.", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Concordia Univ., Montreal, Que., Canada", keywords = "Bessel function; complex zeros; finite element analysis; finite element approximation method; iterative optimisation scheme; modified; poles and zeros", treatment = "T Theoretical or Mathematical", } @Article{Pexton:1979:DRT, author = "Robert L. Pexton and Arno D. Steiger", title = "Degenerate roots of three transcendental equations involving spherical {Bessel} functions", journal = j-MATH-COMPUT, volume = "33", number = "147", pages = "1041--1048", month = jul, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "loose microfiche suppl. 65H10 (65D20)", MRnumber = "80g:65057", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA", keywords = "function approximation; spherical Bessel function; transcendental equation", treatment = "A Application; T Theoretical or Mathematical", } @Article{Phillips:1979:FAC, author = "G. Phillips", title = "A fast approximation to the complementary error function for use in fitting gamma-ray peaks", journal = j-NUCL-INSTR-METH, volume = "164", number = "??", pages = "561--563", month = sep, year = "1979", CODEN = "NUIMAL", DOI = "http://dx.doi.org/10.1016/0029-554X(79)90094-6", ISSN = "0029-554X", URL = "http://adsabs.harvard.edu/abs/1979NucIM.164..561P", abstract = "A fast approximation to the complementary error function has been programmed and tested for use in the peak-shape function for fitting peaks in gamma-ray spectra. The function was compared for speed and accuracy on the NRL ASC 7 computer to the mathematical library version of the complementary error function. The approximation has resulted in a 50\% time savings in the computer program HYPERMET which was developed at NRL for automatic analysis of gamma-ray spectra from germanium detectors.", } @Article{Risch:1979:APE, author = "Robert H. Risch", title = "Algebraic properties of the elementary functions of analysis", journal = j-AM-J-MATH, volume = "101", number = "4", pages = "743--759", year = "1979", CODEN = "AJMAAN", ISSN = "0002-9327", MRclass = "12H05", MRnumber = "81b:12029", MRreviewer = "J. L. Johnson", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Thacher:1979:NBR, author = "Henry C. {Thacher, Jr.}", title = "New Backward Recurrences for {Bessel} Functions", journal = j-MATH-COMPUT, volume = "33", number = "146", pages = "744--764", month = apr, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (33A40)", MRnumber = "81b:65019", MRreviewer = "R. G. Langebartel", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis)", corpsource = "Dept. of Computer Sci., Univ. of Kentucky, Lexington, KY, USA", keywords = "backward recurrences; Bessel functions; converges", treatment = "N New Development; T Theoretical or Mathematical", } @InProceedings{Brent:1980:UAE, author = "R. P. Brent", title = "Unrestricted Algorithms for Elementary and Special Functions", crossref = "Lavington:1980:IPP", pages = "613--619", year = "1980", bibdate = "Thu Sep 01 11:55:31 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Book{Cody:1980:SME, author = "W. J. Cody and W. Waite", title = "Software Manual for the Elementary Functions", publisher = pub-PH, address = pub-PH:adr, pages = "x + 269", year = "1980", ISBN = "0-13-822064-6", ISBN-13 = "978-0-13-822064-8", LCCN = "QA331 .C635 1980", bibdate = "Thu Sep 1 10:12:51 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Ditkin:1980:CSF, author = "V. A. Ditkin and K. A. Karpov and M. K. Kerimov", title = "The computation of special functions", journal = "U.S.S.R. computational mathematics and mathematical physics", volume = "20", number = "5", pages = "3--12", year = "1980", CODEN = "CMMPA9", ISSN = "0041-5553", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.2.1; G.1.2", CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Generating functions; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; design", guideno = "09092", journalabr = "USSR Comput. Math. Math. Phys", jrldate = "1980", subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Fransen:1980:HPV, author = "Arne Frans{\'e}n and Staffan Wrigge", title = "High-precision values of the gamma function and of some related coefficients", journal = j-MATH-COMPUT, volume = "34", number = "150", pages = "553--566", month = apr, year = "1980", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65A05 (65D20)", MRnumber = "81f:65004", MRreviewer = "F. W. J. Olver", bibdate = "Sat Apr 01 10:12:58 2000", bibsource = "JSTOR database", note = "See addendum and corrigendum \cite{Fransen:1981:ACH}.", acknowledgement = ack-nhfb, } @TechReport{Fullerton:1980:BEM, author = "L. W. Fullerton", title = "A Bibliography on the Evaluation of Mathematical Functions", type = "Technical report", number = "TM 80-1274-4 and CSTR 86", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", month = sep, year = "1980", bibdate = "Sat Feb 05 17:39:14 2005", acknowledgement = ack-nhfb, } @InProceedings{Maksymiv:1980:APT, author = "E. M. Maksymiv", booktitle = "Differentsialnye Uravneniya i ikh Prilozhen", title = "Approximate properties of {Thiele}'s formula in a class of elementary functions. ({Russian})", volume = "141", publisher = "Vestnik L'vov. Politekhn. Inst.", address = "L'vov, USSR", pages = "55--56", year = "1980", MRclass = "119.65D20", MRnumber = "81i:65021", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Olver:1980:UAG, author = "F. W. J. Olver", title = "Unrestricted algorithms for generating elementary functions", crossref = "Alefeld:1980:PSE", pages = "131--140", year = "1980", MRclass = "65G05 (65D15)", MRnumber = "82b:65034", MRreviewer = "John Todd", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Tretjakov:1980:PSE, author = "V. A. Tret'jakov", booktitle = "Mathematical analysis and the theory of functions ({Russian}),", title = "On the properties of some elementary functions that are defined on the algebra of bicomplex numbers. ({Russian})", publisher = "Moskov. Oblast. Ped. Inst.,", address = "Moscow, USSR", pages = "99--106", year = "1980", MRclass = "30G35 (78A35)", MRnumber = "82i:30069", MRreviewer = "Toma V. Tonev", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @PhdThesis{vonGudenberg:1980:EAR, author = "J. Wolff {von Gudenberg}", title = "{Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzepts und Implementierung der Standardfunktionen mit optimaler Genauigkeit} \toenglish {Embedding a General Computer Arithmetic in Pascal by Means of an Operator Concept and the Implementation of Elementary Functions with Optimal Accuracy} \endtoenglish", type = "Dissertation", school = "Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1980", bibdate = "Sun Oct 25 10:29:29 1998", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Chen:1981:AFD, author = "Gang Chen", title = "An attempt to find the derivatives of elementary functions using the algorithmic language {BCY}. ({Chinese})", journal = "Zhejiang Daxue Xuebao", volume = "3", pages = "141--149", year = "1981", MRclass = "26A09", MRnumber = "714 524", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Davis:1981:EFA, author = "Diane F. Davis", title = "Elementary Functions on an Array Processor", crossref = "IEEE:1981:PIS", pages = "170--178", year = "1981", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz", acknowledgement = ack-nhfb, } @InProceedings{Farmwald:1981:HBE, author = "P. Michael Farmwald", title = "High Bandwidth Evaluation of Elementary Functions", crossref = "IEEE:1981:PIS", pages = "139--142", year = "1981", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz", acknowledgement = ack-nhfb, } @Article{Fransen:1981:ACH, author = "Arne Frans{\'e}n", title = "Addendum and corrigendum to: {``High-precision values of the gamma function and of some related coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150, 553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}", journal = j-MATH-COMPUT, volume = "37", number = "155", pages = "233--235", month = jul, year = "1981", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65A05 (65D20)", MRnumber = "82m:65002", bibdate = "Sat Apr 01 10:12:58 2000", bibsource = "JSTOR database", note = "See \cite{Fransen:1980:HPV}.", acknowledgement = ack-nhfb, } @TechReport{Fullerton:1981:FUMa, author = "L. W. Fullerton", title = "{FNLIB} User's Manual Explanatory Table of Contents", type = "Technical report", number = "CSTR 92", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", month = mar, year = "1981", bibdate = "Sat Feb 05 17:39:14 2005", acknowledgement = ack-nhfb, } @TechReport{Fullerton:1981:FUMb, author = "L. W. Fullerton", title = "{FNLIB} User's Manual", type = "Technical report", number = "CSTR 95", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", month = mar, year = "1981", bibdate = "Sat Feb 05 17:39:14 2005", acknowledgement = ack-nhfb, } @Article{Glasser:1981:CBS, author = "M. L. Glasser", title = "A Class of {Bessel} Summations", journal = j-MATH-COMPUT, volume = "37", number = "156", pages = "499--501", month = oct, year = "1981", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40 (42A16 44A15)", MRnumber = "82j:33015", MRreviewer = "B. D. Agrawal", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", corpsource = "Dept. of Math. and Computer Sci., Clarkson Coll., Potsdam, NY, USA", keywords = "Bessel functions; Bessel summations; infinite series", treatment = "T Theoretical or Mathematical", } @Article{Hough:1981:API, author = "D. Hough", title = "Application of the proposed {IEEE 754} standard for floating-point arithmetic", journal = j-COMPUTER, volume = "14", number = "3", pages = "70--74", year = "1981", CODEN = "CPTRB4", ISSN = "0018-9162", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz", acknowledgement = ack-nhfb, annote = "Various features of the proposed standard provide an especially convenient environment for programming numerical procedures such as the familiar elementary functions.", bydate = "MB", byrev = "Le", country = "USA", date = "14/06/82", descriptors = "Computer arithmetic; floating point; computation structure; method; application; standard;", enum = "1418", language = "English", location = "RWTH-AC-DFV: Bibl.", references = "10", revision = "21/04/91", } @Article{James:1981:LTS, author = "D. G. James", title = "Linear transformations of the second elementary function", journal = j-LIN-MULT-ALGEBRA, volume = "10", number = "4", pages = "347--349", year = "1981", CODEN = "LNMLAZ", ISSN = "0308-1087", MRclass = "15A69 (10C15)", MRnumber = "83c:15023", MRreviewer = "E. W. Ellers", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Markov:1981:ICE, author = "S. M. Markov", title = "On the interval computation of elementary functions", journal = j-C-R-ACAD-BULGARE-SCI, volume = "34", number = "3", pages = "319--322", year = "1981", CODEN = "DBANAD", ISSN = "0366-8681", MRclass = "65G10", MRnumber = "83e:65084", MRreviewer = "David F. Griffiths", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{McCullagh:1981:RCS, author = "Peter McCullagh", title = "A rapidly convergent series for computing $\psi (z)$ and its derivatives", journal = j-MATH-COMPUT, volume = "36", number = "153", pages = "247--248", month = jan, year = "1981", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (33A15)", MRnumber = "81m:65028", MRreviewer = "J. Gregor", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4120 (Functional analysis)", corpsource = "Imperial Coll. of Sci. and Technol., London, UK", keywords = "(mathematics); convergence; function evaluation; log gamma function; poles; poles and zeros; rapidly convergent series; series; series expansion; uniformly convergent", treatment = "T Theoretical or Mathematical", } @Article{Smith:1981:ERA, author = "J. M. Smith and F. W. J. Olver and D. W. Lozier", title = "Extended-Range Arithmetic and Normalized {Legendre} Polynomials", journal = j-TOMS, volume = "7", number = "1", pages = "93--105", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65G05)", MRnumber = "83a:65017", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355940", acknowledgement = ack-nhfb, keywords = "angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow", } @Article{Steinberg:1981:LSE, author = "D. Steinberg and M. Rodeh", title = "A layout for the shuffle-exchange network with {$O(N^2/\log^{3/2}N)$} area", journal = j-IEEE-TRANS-COMPUT, volume = "C-30", number = "12", pages = "977--982", month = dec, year = "1981", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "C.1.2; G.1.2", CRclass = "C.1.2 Multiple Data Stream Architectures (Multiprocessors); C.1.2 Interconnection architectures; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Interconnection architectures; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "design", guideno = "06519", jrldate = "Dec. 1981", subject = "C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Vogelius:1981:DRM, author = "M. Vogelius and I. Babuska", title = "On a dimensional reduction method. {II}. Some approximation-theoretic results", journal = j-MATH-COMPUT, volume = "37", number = "155", pages = "47--68", month = jul, year = "1981", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G.1.7", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems", genterm = "theory", guideno = "09396", jrldate = "July 1981", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Armengou:1982:ASQ, author = "Santiago Zarzuela Armengou", title = "About some questions of differential algebra concerning to elementary functions", journal = "Publ. Sec. Mat. Univ. Aut{\`o}noma Barcelona", volume = "26", number = "1", pages = "5--15", year = "1982", MRclass = "12H05", MRnumber = "86i:12009", MRreviewer = "Michael F. Singer", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Bazarov:1982:EEF, author = "M. B. Bazarov and Yu. I. Shokin and Z. Kh. Yuldashev", title = "On the Evaluation of Elementary Functions in Interval Analysis (In {Russian})", institution = "Applied Mathematics and Mechanics, Tashkent State Univ.", address = "Tashkent, USSR", pages = "26--31", year = "1982", bibdate = "Fri Jan 12 11:37:56 1996", acknowledgement = ack-jr, } @Article{Belevitch:1982:SIT, author = "V. Belevitch and J. Boersma", title = "On {Stieltjes} integral transforms involving ${\Gamma} $-functions", journal = j-MATH-COMPUT, volume = "38", number = "157", pages = "223--226", month = jan, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "44A15 (33A15 33A45)", MRnumber = "83d:44001", MRreviewer = "V. M. Bhise", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0230 (Integral transforms); C1130 (Integral transforms)", corpsource = "Philips Res Lab., Brussels, Belgium", keywords = "Gamma functions; integral transforms; Stieltjes transforms; systematic classification; transforms", treatment = "T Theoretical or Mathematical", } @Article{Borwein:1982:MNT, author = "P. B. Borwein", title = "On a method of {Newman} and a theorem of {Bernstein}", journal = j-J-APPROX-THEORY, volume = "34", number = "1", pages = "37--41", month = jan, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06012", jrldate = "Jan. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Chambers:1982:UBF, author = "Ll. G. Chambers", title = "An upper bound for the first zero of {Bessel} functions", journal = j-MATH-COMPUT, volume = "38", number = "158", pages = "589--591", month = apr, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A65", MRnumber = "83h:33011", MRreviewer = "S. Ahmed", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Cody:1982:TTP, author = "W. J. Cody", title = "Transportable test procedures for elementary function software", crossref = "Mulvey:1982:EMP", pages = "236--247", year = "1982", bibdate = "Thu Nov 17 06:39:08 1994", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", acknowledgement = ack-wjc, } @Article{Crick:1982:IRB, author = "S. E. Crick", title = "Inclusion relations for {Bernstein} quasi-analytic classes", journal = j-J-APPROX-THEORY, volume = "34", number = "4", pages = "375--379", month = apr, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "07841", jrldate = "April 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Cruz:1982:ZHF, author = "Andr{\'e}s Cruz and Javier Sesma", title = "Zeros of the {Hankel} function of real order and of its derivative", journal = j-MATH-COMPUT, volume = "39", number = "160", pages = "639--645", month = oct, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40", MRnumber = "83j:33005", MRreviewer = "S. Ahmed", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); B0290F (Interpolation and function approximation); C4120 (Functional analysis); C4130 (Interpolation and function approximation)", corpsource = "Dept. de Fisica Teorica, Univ. de Zaragoza, Zaragoza, Spain", keywords = "approximation; derivative; evaluation; function approximation; function evaluation; Hankel function; poles and zeros; real order; trajectories; zeros", treatment = "T Theoretical or Mathematical", } @Article{Danielopoulos:1982:CEP, author = "S. D. Danielopoulos", title = "On the Cost of Evaluating Polynomials and Their Derivatives", journal = j-COMPUTING, volume = "29", number = "4", pages = "373--380", year = "1982", CODEN = "CMPTA2", ISSN = "0010-485X (printed version), 1436-5057 (electronic version)", MRclass = "68C25 (68C20)", MRnumber = "84a:68039", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "Compendex database; MathSciNet database; ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ of Ioannina, Greece", catcode = "G.1.2; G.4; G.1.0", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Algorithm analysis; G.1.0 General; G.1.0 Computer arithmetic", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic", genterm = "economics; theory", guideno = "04049", journalabr = "Computing (Vienna/New York)", jrldate = "1982", keywords = "mathematical techniques", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Epstein:1982:UAF, author = "C. Epstein and W. L. Miranker and T. J. Rivlin", title = "Ultra-arithmetic {I}: function data types", journal = j-MATH-COMP-SIM, volume = "24", number = "1", pages = "1--18", month = feb, year = "1982", CODEN = "MCSIDR", ISSN = "0378-4754", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1; G.1.2; G.1.2", CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.2 Approximation; G.1.2 Chebyshev approximation and theory; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms", guideno = "09324", jrldate = "Feb. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Epstein:1982:UAI, author = "C. Epstein and W. L. Miranker and T. J. Rivlin", title = "Ultra-arithmetic {II}: intervals of polynomials", journal = j-MATH-COMP-SIM, volume = "24", number = "1", pages = "19--29", month = feb, year = "1982", CODEN = "MCSIDR", ISSN = "0378-4754", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G.1.1; G.1.0", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.1 Interpolation; G.1.1 Spline and piecewise polynomial interpolation; G.1.0 General; G.1.0 Error analysis", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation; Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis", genterm = "algorithms", guideno = "09325", jrldate = "Feb. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Gawronski:1982:ACF, author = "W. Gawronski and U. Stadtm{\"u}ller", title = "Approximation of continuous functions by generalized {Favard} operators", journal = j-J-APPROX-THEORY, volume = "34", number = "4", pages = "384--396", month = apr, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; algorithms", guideno = "06038", jrldate = "April 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Gordon:1982:RAN, author = "H. T. Gordon", title = "Rough approximation numerical algorithms", journal = j-DDJ, volume = "7", number = "7", pages = "54--56", month = jul, year = "1982", CODEN = "DDJOEB", ISSN = "1044-789X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991); http://www.ddj.com/index/author/index.htm", acknowledgement = ack-nhfb, catcode = "G.1.0; G.1.2", CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", guideno = "04547", jrldate = "July 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Greaves:1982:AHM, author = "G. Greaves", title = "An algorithm for the {Hausdorff} moment problem", journal = j-NUM-MATH, volume = "39", number = "2", pages = "231--238", month = aug, year = "1982", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms", guideno = "07489", jrldate = "Aug. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @TechReport{Kahan:1982:BCC, author = "W. Kahan", title = "Branch Cuts for Complex Elementary Functions", type = "Technical Report", number = "PAM-105", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, year = "1982", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz", acknowledgement = ack-nhfb, keywords = "na, elementary function", } @Article{Keener:1982:CLB, author = "L. L. Keener", title = "Characterizing local best {SAIN} approximations", journal = j-J-APPROX-THEORY, volume = "36", number = "1", pages = "55--63", month = sep, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Chebyshev approximation and theory; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06074", jrldate = "Sept. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Lassey:1982:CCI, author = "Keith R. Lassey", title = "On the computation of certain integrals containing the modified {Bessel} function ${I}_{0}(\xi )$", journal = j-MATH-COMPUT, volume = "39", number = "160", pages = "625--637", month = oct, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20", MRnumber = "83j:65029", MRreviewer = "Walter Gautschi", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); B0290M (Numerical integration and differentiation); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Inst. of Nuclear Sci., DSIR, Lower Hutt, New Zealand", keywords = "approximation; approximation theory; convergence of numerical methods; convergent series; function; function approximation; integration; limiting behaviour; modified Bessel; numerical integration; one-dimensional integrals; two-dimensional integrals", treatment = "T Theoretical or Mathematical", } @Article{Ling:1982:EIH, author = "Chih Bing Ling and Ming Jing Wu", title = "Evaluation of integrals of {Howland} type involving a {Bessel} function", journal = j-MATH-COMPUT, volume = "38", number = "157", pages = "215--222", month = jan, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65A05 (65D20)", MRnumber = "82m:65003", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); B0290M (Numerical integration and differentiation); C1120 (Mathematical analysis); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Maths., Virginia Polytech. Inst. and State Univ., Blacksburg, VA, USA", keywords = "10D; 20D; accuracy; Bessel function; Bessel functions; Howland type; integrals; integration; tabulated values", treatment = "T Theoretical or Mathematical", } @InCollection{Mori:1982:ARS, author = "S. Mori and C. Y. Suen", editor = "Ching Y. Suen and Renato De Mori", key = "Scanners", booktitle = "Computer analysis and perception: vol. I, Visual signals", title = "Automatic recognition of symbols and architecture of the recognition unit", publisher = pub-CRC, address = pub-CRC:adr, pages = "17--40", year = "1982", ISBN = "0-8493-6305-5 (vol. 1), 0-8493-6306-3 (vol. 2)", ISBN-13 = "978-0-8493-6305-4 (vol. 1), 978-0-8493-6306-1 (vol. 2)", LCCN = "TA1650 .C65 1982", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bookpages = "various", catcode = "I.5; G.1.2; C.3; B.7; I.5.4", CRclass = "I.5.2 Design Methodology; G.1.2 Approximation; G.1.2 Elementary function approximation; C.3 Signal processing systems; B.7.1 Types and Design Styles; I.5.4 Applications; I.5.4 Signal processing", descriptor = "Computing Methodologies, PATTERN RECOGNITION, Design Methodology; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Computer Systems Organization, SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal processing systems; Hardware, INTEGRATED CIRCUITS, Types and Design Styles; Computing Methodologies, PATTERN RECOGNITION, Applications, Signal processing", genterm = "documentation; theory; design", guideno = "01691", subject = "I. Computing Methodologies; I.5 PATTERN RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C. Computer Systems Organization; C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS; B. Hardware; B.7 INTEGRATED CIRCUITS; I. Computing Methodologies; I.5 PATTERN RECOGNITION", } @Article{Ollin:1982:CFE, author = "H. Z. Ollin and I. Gerst", title = "Classes of functions with explicit best uniform approximations", journal = j-J-APPROX-THEORY, volume = "34", number = "3", pages = "264--276", month = mar, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06030", jrldate = "March 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Rack:1982:GIV, author = "H.-J Rack", title = "A generalization of an inequality of {V. Markov} to multivariate polynomials", journal = j-J-APPROX-THEORY, volume = "35", number = "1", pages = "94--97", month = may, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06047", jrldate = "May 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @PhdThesis{Rockey:1982:DMS, author = "S. A. Rockey", title = "Discrete methods of state approximation, parameter identification and optimal control for hereditary systems", type = "{Ph.D} Thesis", school = "Brown University", address = "Providence, RI", pages = "208", year = "1982", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G.1.2; G.1.5", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Linear approximation; G.1.5 Roots of Nonlinear Equations; G.1.5 Convergence", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence", guideno = "15449", source = "UMI order no. DA8228325", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Sommer:1982:EPL, author = "M. Sommer", title = "Existence of pointwise-{Lipschitz}-continuous selections of the metric projection for a class of {$Z$}-spaces", journal = j-J-APPROX-THEORY, volume = "34", number = "2", pages = "115--130", month = feb, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06018", jrldate = "Feb. 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @PhdThesis{Wang:1982:AME, author = "J.-L Wang", title = "Asymptotically minimax estimators for distributions with increasing failure rate", type = "{Ph.D} Thesis", school = "University of California, Berkeley", address = "Berkeley, CA, USA", pages = "42", year = "1982", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "design", guideno = "15084", source = "UMI order no. DA8300696", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Whitley:1982:MBI, author = "R. Whitley", title = "{Markov} and {Bernstein}'s inequalities, and compact and strictly singular operators", journal = j-J-APPROX-THEORY, volume = "34", number = "3", pages = "277--285", month = mar, year = "1982", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "06031", jrldate = "March 1982", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Wills:1982:RCA, author = "C. A. Wills and J. M. Blair and P. L. Ragde", title = "Rational {Chebyshev} approximations for the {Bessel} functions ${J}_{0}(x)$, ${J}_{1}(x)$, ${Y}_{0}(x)$, ${Y}_{1}(x)$", journal = j-MATH-COMPUT, volume = "39", number = "160", pages = "617--623", month = oct, year = "1982", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (33A40 41A50)", MRnumber = "83j:65030", MRreviewer = "C. W. Clenshaw", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0260 (Optimisation techniques); B0290F (Interpolation and function approximation); C1180 (Optimisation techniques); C4130 (Interpolation and function approximation)", corpsource = "AEG Ltd., Chalk River Nuclear Labs., Ont., Canada", keywords = "approximations; Bessel functions; Chebyshev; Chebyshev approximation; formulae; McMahon asymptotic; minimax techniques; near-minimax rational approximation", treatment = "T Theoretical or Mathematical", } @Article{Benton:1983:CZT, author = "T. C. Benton", title = "Common Zeros of Two {Bessel} Functions. Part {II}. Approximations and Tables", journal = j-MATH-COMPUT, volume = "41", number = "163", pages = "203--217", month = jul, year = "1983", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40 (65A05)", MRnumber = "85a:33010", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", corpsource = "Dept. of Math., Pennsylvania State Univ., University Park, PA, USA", keywords = "Bessel functions; computer program; poles and zeros", treatment = "T Theoretical or Mathematical", } @Article{Cash:1983:BRKa, author = "J. R. Cash", title = "Block {Runge--Kutta} Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations. Part {I}. The Nonstiff Case", journal = j-MATH-COMPUT, volume = "40", number = "161", pages = "175--191", month = jan, year = "1983", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65L05", MRnumber = "84d:65044a", MRreviewer = "W. C. Rheinboldt", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); B0290M (Numerical integration and differentiation); B0290P (Differential equations); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation); C4170 (Differential equations)", corpsource = "Dept. of Math., Imperial Coll., London, UK", keywords = "approximate numerical integration; approximation theory; block implicit formulae; block Runge--Kutta formulae; C. W. Gear; differential equations; equations; first order; formulae; initial value; initial value problems; integration; linear multistep methods; nonstiff problems; order; ordinary differential; problems; Runge--Kutta methods; Runge--Kutta starters; stepsize; stiff problems; systems; variable order; variable order block explicit", treatment = "T Theoretical or Mathematical", } @Article{Cody:1983:ASM, author = "W. J. Cody", title = "Algorithm 597: Sequence of Modified {Bessel} Functions of the First Kind", journal = j-TOMS, volume = "9", number = "2", pages = "242--245", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MISCELLANEOUS", genterm = "algorithms", guideno = "02186", jrldate = "June 1983", keywords = "algorithms", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation G Mathematics of Computing, MISCELLANEOUS", } @Article{Coleman:1983:CEB, author = "J. P. Coleman and A. J. Monaghan", title = "{Chebyshev} expansions for the {Bessel} function ${J}_{n}(z)$ in the complex plane", journal = j-MATH-COMPUT, volume = "40", number = "161", pages = "343--366", month = jan, year = "1983", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65A05 (30E10 33A40 65D20)", MRnumber = "84c:65013", MRreviewer = "C. W. Clenshaw", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Cruz:1983:MPR, author = "Andr{\'e}s Cruz and Javier Sesma", title = "Modulus and phase of the reduced logarithmic derivative of the {Hankel} function", journal = j-MATH-COMPUT, volume = "41", number = "164", pages = "597--605", month = oct, year = "1983", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40 (65H05 81F10)", MRnumber = "85b:33006", MRreviewer = "H. E. Fettis", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Ellacott:1983:FTE, author = "S. W. Ellacott", title = "On the {Faber} transform and efficient numerical rational approximation", journal = j-SIAM-J-NUMER-ANAL, volume = "20", number = "5", pages = "989--1000", month = oct, year = "1983", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", MRclass = "41A20 (41A21)", MRnumber = "85f:41010", MRreviewer = "Lee L. Keener", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Fukushima:1983:OAA, author = "M. Fukushima", title = "An outer approximation algorithm for solving general convex programs", journal = j-OPER-RES, volume = "31", number = "1", pages = "101--113", month = feb, year = "1983", CODEN = "OPREAI", ISSN = "0030-364X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2; G.4", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Efficiency", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency", genterm = "algorithms; documentation; performance; reliability; theory", guideno = "09992", jrldate = "Jan./Feb. 1983", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE", } @Article{Giordano:1983:EAZ, author = "C. Giordano and A. Laforgia", title = "Elementary approximations for zeros of {Bessel} functions", journal = j-J-COMP-APPL-MATH, volume = "9", number = "3", pages = "221--228", month = sep, year = "1983", CODEN = "JCAMDI", ISSN = "0377-0427", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "08115", jrldate = "Sept. 1983", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Hasson:1983:C, author = "M. Hasson and O. Shisha", title = "On the condition $\sum^{\infty}_{n=1}n^{p-1}{E}^{*}_{n}(f) < \infty$", journal = j-J-APPROX-THEORY, volume = "39", number = "4", pages = "389--398", month = dec, year = "1983", CODEN = "JAXTAZ", ISSN = "0021-9045", MRclass = "42A10 (41A10)", MRnumber = "85a:42002", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", note = "See corrigendum \cite{}.", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "07952", jrldate = "Dec. 1983", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Kershaw:1983:SEW, author = "D. Kershaw", title = "Some extensions of {W. Gautschi}'s inequalities for the gamma function", journal = j-MATH-COMPUT, volume = "41", number = "164", pages = "607--611", month = oct, year = "1983", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A15 (26D20 65D20)", MRnumber = "84m:33003", MRreviewer = "P. Anandani", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Lehnhoff:1983:NPT, author = "H.-G Lehnhoff", title = "A new proof of {Teljakowskii}'s theorem", journal = j-J-APPROX-THEORY, volume = "38", number = "2", pages = "177--181", month = jun, year = "1983", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "07897", jrldate = "June 1983", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Lehnhoff:1983:SPF, author = "H.-G Lehnhoff", title = "A simple proof of a {A.F. Timan}'s theorem", journal = j-J-APPROX-THEORY, volume = "38", number = "2", pages = "172--176", month = jun, year = "1983", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "07896", jrldate = "June 1983", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Little:1983:CCS, author = "F. Little", editor = "Robert E. Barnhill and Wolfgang Boehm", booktitle = "Surfaces in computer aided geometric design: proceedings of a conference held at Mathematisches Forschungsinstitut Oberwolfach, F.R.G., April 25--30, 1982, organized by Wolfgang Boehm and Josef Hoschek", title = "Convex combination surfaces", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "99--109", year = "1983", ISBN = "0-444-86550-0", ISBN-13 = "978-0-444-86550-2", LCCN = "T385 .S827 1982", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bookpages = "xvi + 215", catcode = "G.1.1; G.1.1; G.1.2", CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas; G.1.1 Interpolation; G.1.1 Smoothing; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory", guideno = "13093", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @TechReport{Lutskii:1983:VFT, author = "G. M. Lutski{\u{\i}} and O. I. Penchev", title = "{\cyr Vychislenie {\`e}lementarnykh funktsi{\u{\i}}metodom tsifra za tsifro{\u{\i}}v izbytochnykh sistemakh schisleniya}. ({Russian}) [Calculation of elementary functions by the digit-by-digit method in redundant number systems]", type = "Preprint", number = "83-22", institution = "Akad. Nauk Ukrain. SSR, Inst. Kibernet.", address = "Kiev, USSR", pages = "30", year = "1983", MRclass = "65D20", MRnumber = "719 021", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{McCurdy:1983:ACD, author = "A. McCurdy and K. C. Ng and Beresford N. Parlett", title = "Accurate computation of divided differences of the exponential function", type = "Report", number = "PAM-160", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1983", bibdate = "Fri Nov 11 09:06:19 2005", acknowledgement = ack-nhfb, } @Article{Meister:1983:MYF, author = "B. Meister", title = "On {Murphy}'s yield formula", journal = j-IBM-JRD, volume = "27", number = "6", pages = "545--548", month = nov, year = "1983", CODEN = "IBMJAE", ISSN = "0018-8646", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "B.7.1; G.1.2", CRclass = "B.7.1 Types and Design Styles; B.7.1 Input/Output circuits; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design Styles, Input/Output circuits; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; design; reliability", guideno = "06316", jrldate = "Nov. 1983", subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @PhdThesis{Monk:1983:SFE, author = "P. B. Monk", title = "Some finite element methods for the approximation of the biharmonic equation", type = "{Ph.D} Thesis", school = "Rutgers University, The State University of New Jersey", address = "New Brunswick, NJ, USA", pages = "242", year = "1983", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.8; G.1.2", CRclass = "G.1.8 Partial Differential Equations; G.1.8 Finite element methods; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "design; algorithms; experimentation", guideno = "15929", source = "UMI order no. DA8308441", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Nave:1983:ITF, author = "Rafi Nave", key = "Nav83", title = "Implementation of Transcendental Functions on a Numerics Processor", journal = j-MICROPROC-MICROPROG, volume = "11", pages = "221--225", year = "1983", CODEN = "MMICDT", ISSN = "0165-6074", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz", acknowledgement = ack-nhfb, } @Article{Volz:1983:CAA, author = "H. V{\"o}lz", title = "{{CORDIC} und {\"a}hnliche Algorithmen der elementaren Funktionen mit besonderer Eignung f{\"u}r Mikrorechner} \toenglish {CORDIC and Similar Algorithms for Elementary Functions with Particular Aptitude for Microcomputers} \endtoenglish", journal = j-NACH-ELEK, volume = "33", number = "12", pages = "506--510", month = "????", year = "1983", CODEN = "NTELAP", ISSN = "0323-4657", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Xu:1983:HPG, author = "Xian Yu Xu and Jia Kai Li and Gui Jing Xiong and Guo Liang Xu and Chun Qing Lu", title = "High-precision generation of elementary functions. ({Chinese})", journal = "Appl. Math. Math. Comput.", volume = "6", pages = "24--32", year = "1983", MRclass = "65D20", MRnumber = "86e:65031", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Berges:1984:AFE, author = "J. C. Berges", booktitle = "Space mathematics", title = "Arithm{\'e}tique et fonctions {\'e}l{\'e}mentaires sur mini-micro calculateurs. ({French}) [Arithmetic and elementary functions on mini-micro computers]", publisher = "C{\'e}padu{\`e}s", address = "Toulouse, France", pages = "193--229", year = "1984", MRclass = "65-01 (65-04)", MRnumber = "849 200", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Black:1984:NIS, author = "Cheryl M. Black and Robert P. Burton and Thomas H. Miller", title = "The Need for an Industry Standard of Accuracy for Elementary-Function Programs", journal = j-TOMS, volume = "10", number = "4", pages = "361--366", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "792 000", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, catcode = "G.1.0; G.1.2; G.4", CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Efficiency", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency", genterm = "theory; algorithms; reliability; standardization", guideno = "02897", jrldate = "Dec. 1984", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE", } @Article{Borwein:1984:AGM, author = "J. M. Borwein and P. B. Borwein", title = "The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions", journal = j-SIAM-REVIEW, volume = "26", number = "3", pages = "351--366", month = jul, year = "1984", CODEN = "SIREAD", ISSN = "0036-1445", MRclass = "65D20 (26A09)", MRnumber = "86d:65029", MRreviewer = "S. Conde", bibdate = "Mon Jan 20 10:31:25 MST 1997", bibsource = "Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", abstract = "We produce a self contained account of the relationship between the Gaussian arithmetic-geometric mean iteration and the fast computation of elementary functions. A particularly pleasant algorithm for pi is one of the by-products.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliationaddress = "Dalhousie Univ, Halifax, NS, Can", classification = "921; 723", journalabr = "SIAM Rev", keywords = "arithmetic-geometric mean; calculation of pi; computational methods; elliptic functions; Iterative Methods; mathematical techniques; numerical mathematics", } @Article{Fransen:1984:CMM, author = "Arne Frans{\'e}n and Staffan Wrigge", title = "Calculation of the moments and the moment generating function for the reciprocal gamma distribution", journal = j-MATH-COMPUT, volume = "42", number = "166", pages = "601--616", month = apr, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (60E10 62E15 65U05)", MRnumber = "86f:65042a", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C1210B (Reliability theory); C4130 (Interpolation and function approximation)", corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden", keywords = "kurtosis; moment generating function; moments; polynomials; reciprocal gamma distribution; reliability theory; skewness; variance", treatment = "T Theoretical or Mathematical", } @Article{Glaeske:1984:LTS, author = "H.-J. Glaeske and O. I. Mari{\v{c}}ev", title = "The {Laguerre} transform of some elementary functions", journal = j-Z-ANAL-ANWEND, volume = "3", number = "3", pages = "237--244", year = "1984", ISSN = "0232-2064", MRclass = "44A15 (34A10)", MRnumber = "86a:44005", MRreviewer = "Ram Kishore Saxena", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Laforgia:1984:FIG, author = "Andrea Laforgia", title = "Further Inequalities for the Gamma Function", journal = j-MATH-COMPUT, volume = "42", number = "166", pages = "597--600", month = apr, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A15", MRnumber = "85i:33001", MRreviewer = "H. E. Fettis", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Math., Univ. of Torino, Torino, Italy", keywords = "gamma function; inequalities; polynomials", treatment = "T Theoretical or Mathematical", } @Article{McCurley:1984:EE, author = "Kevin S. McCurley", title = "Explicit Estimates for $\theta (x; 3, l)$ and $\psi (x; 3, l)$", journal = j-MATH-COMPUT, volume = "42", number = "165", pages = "287--296", month = jan, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "11N56", MRnumber = "85g:11085", MRreviewer = "G. J. Rieger", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Maths., Michigan State Univ., East Lansing, MI, USA", keywords = "arithmetic progressions; Chebyshev approximation; Chebyshev functions; Dirichlet L-; explicit estimates; functions; prime number; theorem; zeros", treatment = "T Theoretical or Mathematical", } @Article{Newman:1984:ABS, author = "J. N. Newman", title = "Approximations for the {Bessel} and {Struve} functions", journal = j-MATH-COMPUT, volume = "43", number = "168", pages = "551--556", month = oct, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (33A40)", MRnumber = "86c:65021", MRreviewer = "S. Conde", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C1120 (Mathematical analysis); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Ocean Eng., MIT, Cambridge, MA, USA", keywords = "accuracy; Bessel functions; function approximation; functions; IBM PC computer; minimax; polynomial approximations; polynomials; rational-fraction approximations; single-precision computations; Struve", treatment = "T Theoretical or Mathematical", } @TechReport{Ng:1984:DAA, author = "K. C. Ng", title = "Contributions to the computation of the matrix exponential", type = "Report", number = "PAM-212", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = feb, year = "1984", bibdate = "Fri Nov 11 09:06:19 2005", note = "Based on the author's Ph.D. thesis.", acknowledgement = ack-nhfb, keywords = "$\exp(Bt)$", } @Article{Nishimoto:1984:TFD, author = "Katsuyuki Nishimoto", title = "Tables of fractional differintegrations of elementary functions", journal = "J. College Engrg. Nihon Univ. Ser. B", volume = "25", pages = "41--46", year = "1984", ISSN = "0285-6182", MRclass = "30E20 (26A33)", MRnumber = "85f:30065", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Piessens:1984:SEF, author = "R. Piessens", title = "A Series Expansion for the First Positive Zero of the {Bessel} Functions", journal = j-MATH-COMPUT, volume = "42", number = "165", pages = "195--197", month = jan, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40 (65D20)", MRnumber = "84m:33014", MRreviewer = "M. E. Muldoon", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database; Theory/Comp.Alg.1.bib", acknowledgement = ack-nhfb, annote = "Gives explicit series for first positive zero for 4 terms, using REDUCE.", classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", corpsource = "Dept. of Computer Sci., Univ. of Leuven, Heverlee, Belgium", keywords = "Bessel functions; poles and zeros; positive zero; Reduce; series (mathematics); series expansion", treatment = "T Theoretical or Mathematical", } @Article{vonGudenberg:1984:BMG, author = "J. Wolff {von Gudenberg}", title = "{Berechnung maximal genauer Standardfunktionen mit einfacher Mantissenl{\"a}nge} \toenglish {Computation of Maximally Accurate Elementary Functions Using Simple Mantissa Length} \endtoenglish", journal = j-ELEK-RECHENANLAGEN, volume = "26", number = "5", pages = "230--238", month = oct, year = "1984", CODEN = "ELRAA4", ISSN = "0013-5720", bibdate = "Sun Oct 25 10:29:27 1998", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Wrigge:1984:NMG, author = "Staffan Wrigge", title = "A note on the moment generating function for the reciprocal gamma distribution", journal = j-MATH-COMPUT, volume = "42", number = "166", pages = "617--621", month = apr, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D20 (60E10 62E15 65U05)", MRnumber = "86f:65042b", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden", keywords = "Euler-Maclaurin expansion; moment generating function; polynomials; reciprocal gamma distribution", treatment = "T Theoretical or Mathematical", } @Article{Akrivis:1985:ENC, author = "G. Akrivis", title = "The error norm of certain {Gaussian} quadrature formulae", journal = j-MATH-COMPUT, volume = "45", number = "172", pages = "513--519", month = oct, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D32", MRnumber = "87a:65051", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290B (Error analysis in numerical methods); B0290F (Interpolation and function approximation); C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)", corpsource = "Math. Inst., Munchen Univ., West Germany", keywords = "error analysis; error functional; error norm; function approximation; Gaussian quadrature formulae; integration; weight functions; wide class", treatment = "T Theoretical or Mathematical", } @Article{Frenzen:1985:NAE, author = "C. L. Frenzen and R. Wong", title = "A note on asymptotic evaluation of some {Hankel} transforms", journal = j-MATH-COMPUT, volume = "45", number = "172", pages = "537--548", month = oct, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "41A60 (44A15 65R10)", MRnumber = "87c:41024", MRreviewer = "F. W. J. Olver", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0230 (Integral transforms); B0290Z (Other numerical methods)C1130 (Integral transforms); C4190 (Other numerical methods)", corpsource = "Dept. of Math., British Columbia Univ., Vancouver, BC, Canada", keywords = "asymptotic expansion; Bessel function; Bessel functions; growth condition; Hankel transforms; meromorphic function; transforms", treatment = "T Theoretical or Mathematical", } @InProceedings{Gal:1985:CEF, author = "Shmuel Gal", title = "Computing Elementary Functions: {A} New Approach for Achieving High Accuracy and Good Performance", crossref = "Miranker:1985:ASC", pages = "1--16", year = "1985", bibdate = "Sat Nov 09 07:42:53 2002", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Hull:1985:PRV, author = "T. E. Hull and A. Abrham", title = "Properly Rounded Variable Precision Square Root", journal = j-TOMS, volume = "11", number = "3", pages = "229--237", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15 (65G05)", MRnumber = "87a:65041", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/214413.html; http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/", abstract = "The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. {\em Properly rounded} means rounded to the nearest, or to nearest even in case of a tie. It is {\em variable precision} in that it is designed to return a $p$-digit approximation to a $p$-digit argument, for any $p$ \$>\$ 0. (Precision $p$ means $p$ decimal digits.) The program and the analysis are valid for all $p$ \$>\$ 0, but current implementations place some restrictions on $p$.", acknowledgement = ack-nhfb, catcode = "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0", CRclass = "G.4 Algorithm analysis; G.4 Verification; G.1.0 General; G.1.0 Numerical algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Certification and testing; G.1.0 General; G.1.0 Error analysis", descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification; Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing; Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis", genterm = "algorithms; verification", guideno = "02789", jrldate = "Sept. 1985", keywords = "algorithms; verification", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Kravchuk:1985:ACE, author = "V. R. Kravchuk", title = "Approximation of certain elementary functions by rational functions of order $(n,2)$. ({Russian})", journal = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint", volume = "18", pages = "7--40", year = "1985", MRclass = "41A25 (41A10)", MRnumber = "87b:41017", MRreviewer = "R. Smarzewski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Kravchuk:1985:EAE, author = "V. R. Kravchuk", title = "Effective approximation of elementary functions by rational polynomials of order $(n,1)$. ({Russian})", journal = "Ukrain. Mat. Zh.", volume = "37", number = "2", pages = "175--180, 270", year = "1985", MRclass = "41A20 (41A25)", MRnumber = "86h:41013", MRreviewer = "Miguel A. Jim{\'e}nez Pozo", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Lazard:1985:PFD, author = "Daniel Lazard", title = "Primitives des fonctions {\'e}l{\'e}mentaires (d'apr{\`e}s {Risch} et {Davenport}). ({French}) [Primitives of elementary functions (following {Risch} and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No. 121-122}", journal = "Ast{\'e}risque", volume = "121--122", pages = "295--308", year = "1985", MRclass = "12H05 (12-04)", MRnumber = "86k:12010", MRreviewer = "J. H. Davenport", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Milgram:1985:GIE, author = "M. S. Milgram", title = "The Generalized Integro-Exponential Function", journal = j-MATH-COMPUT, volume = "44", number = "170", pages = "443--458", month = apr, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A70 (65D15)", MRnumber = "86c:33024", MRreviewer = "S. Conde", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); B0290F (Interpolation and function approximation); C4120 (Functional analysis); C4130 (Interpolation and function approximation)", corpsource = "AECL, Chalk River, Ont., Canada", keywords = "exponential function; exponential integral; first-order functions; function; function approximation; function evaluation; generalized integro-; incomplete gamma; minimax; rational minimax approximations; techniques", treatment = "T Theoretical or Mathematical", } @Article{Muller:1985:DBC, author = "Jean-Michel Muller", title = "Discrete basis and computation of elementary functions", journal = j-IEEE-TRANS-COMPUT, volume = "34", number = "9", pages = "857--862", year = "1985", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "65D20 (65V05)", MRnumber = "87e:65016", MRreviewer = "D. Zwick", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Muller:1985:RNR, author = "Jean-Michel Muller", booktitle = "Seminar on number theory, 1984--1985 (Talence, 1984/1985),", title = "Repr{\'e}sentation des nombres r{\'e}els et calcul des fonctions {\'e}l{\'e}mentaires. ({French}) [Representation of real numbers and calculation of elementary functions]", volume = "12", publisher = "Univ. Bordeaux {I}", address = "Talence, France", pages = "22", year = "1985", MRclass = "26-04 (11B13 11B34 26A09)", MRnumber = "87k:26001", MRreviewer = "S. L. Segal", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, remark = "From the MRreview: ``About one third of the paper is devoted to algorithms for calculating quantities like square root, exponential, logarithm, or trigonometric funtions, using discrete bases. Indeed, the major motivation for the present paper is obtaining simple algorithms which can easily be realized by hardware.''", } @TechReport{Parlett:1985:DAA, author = "Beresford N. Parlett and K. C. Ng", title = "Development of an accurate algorithm for {$\exp(Bt)$}", type = "Technical Report", number = "PAM-294", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = aug, year = "1985", bibdate = "Fri Nov 11 09:06:19 2005", acknowledgement = ack-nhfb, } @Article{Pereira:1985:ECF, author = "N. Costa Pereira", title = "Estimates for the {Chebyshev} function $\psi(x)-\theta (x)$", journal = j-MATH-COMPUT, volume = "44", number = "169", pages = "211--221", month = jan, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "11A25 (11N45 11Y35 33A70)", MRnumber = "86k:11005", bibdate = "Thu Jun 15 07:26:46 2000", bibsource = "JSTOR database", note = "See corrigendum \cite{Pereira:1987:CEC}.", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", keywords = "Chebyshev approximation; Chebyshev function", treatment = "T Theoretical or Mathematical", } @Article{Spijker:1985:SRS, author = "M. N. Spijker", title = "Stepsize restrictions for stability of one-step methods in the numerical solution of initial value problems", journal = j-MATH-COMPUT, volume = "45", number = "172", pages = "377--392", month = oct, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65L20 (65M10)", MRnumber = "86j:65106", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "A0260 (Numerical approximation and analysis); A0560 (Transport processes: theory); B0290F (Interpolation and function approximation); B0290P (Differential equations); C4130 (Interpolation and function approximation); C4170 (Differential equations); C7320 (Physics and chemistry computing)", corpsource = "Inst. of Appl. Math. and Comput. Sci., Leiden Univ., Netherlands", keywords = "convection; convergence of numerical methods; differential equations; diffusion; diffusion-convection; error growth; initial value problems; iterative methods; numerical solution; partial; problem; stability of one-step methods; stepsize restrictions", treatment = "T Theoretical or Mathematical", } @Article{Agarwal:1986:NSV, author = "Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman", title = "New Scalar and Vector Elementary Functions for the {IBM System\slash 370}", journal = j-IBM-JRD, volume = "30", number = "2", pages = "126--144", month = mar, year = "1986", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "76W05", MRnumber = "840 341", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "Compendex database", note = "See clarification \cite{Agarwal:1987:CNS}.", abstract = "Algorithms have been developed to compute short-and long-precision elementary functions: SIN, COS, TAN, COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS, ATAN2, and CABS, in scalar (28 functions) and vector (22 functions) mode. They have been implemented as part of the new VS FORTRAN library recently announced along with the IBM 3090 Vector Facility. These algorithms are essentially table-based algorithms. An important feature of these algorithms is that they produce bitwise-identical results on scalar and vector System\slash 370 machines. Of these, for five functions the computed value result is always the correctly rounded value of the infinite-precision result. For the rest of the functions, the value returned is one of the two floating-point neighbors bordering the infinite-precision result, which implies exact results if they are machine-representable. For the five correctly rounded elementary functions, scalar and vector algorithms are designed independently to optimize performance in each case.", acknowledgement = ack-nhfb, classification = "723", journalabr = "IBM J Res Dev", keywords = "algorithms; Algorithms; computer metatheory; computer programming; computer programming languages --- fortran; design; elementary functions; fortran library; IBM System/370; infinite-precision result; measurement; performance; table-based algorithms", subject = "C.4 Computer Systems Organization, PERFORMANCE OF SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms \\ F.3.3 Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Functional constructs \\ C.1.2 Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors", } @Article{Bustoz:1986:GFI, author = "Joaquin Bustoz and Mourad E. H. Ismail", title = "On Gamma Function Inequalities", journal = j-MATH-COMPUT, volume = "47", number = "176", pages = "659--667", month = oct, year = "1986", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A15 (26D20)", MRnumber = "87m:33002", MRreviewer = "G. Gasper", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1130 (Integral transforms); C1140Z (Other and miscellaneous)", corpsource = "Dept. of Math., Arizona State Univ., Tempe, AZ, USA", keywords = "gamma function inequalities; infinite divisibility; Laplace; Laplace transforms; monotonic functions; probability; probability distributions; quotients; transforms", treatment = "T Theoretical or Mathematical", } @Article{Clenshaw:1986:GEL, author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner", title = "Generalized Exponential and Logarithmic Functions", journal = j-COMP-MATH-APPL-B, volume = "12B", number = "5--6", pages = "1091--1101", month = "????", year = "1986", CODEN = "CMAPDK", ISSN = "0886-9561", MRclass = "33A70 (39B10 65G05)", MRnumber = "MR0871348 (88a:33027)", bibdate = "Fri Jul 09 06:27:26 2004", acknowledgement = ack-nhfb, } @Article{Evans:1986:RIU, author = "D. J. Evans and G. M. Megson", title = "{Romberg} integration using systolic arrays", journal = j-PARALLEL-COMPUTING, volume = "3", number = "4", pages = "289--304", month = oct, year = "1986", CODEN = "PACOEJ", ISSN = "0167-8191", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "11019", catcode = "G.1.1; G.1.2", CRclass = "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Extrapolation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; design; algorithms", guideno = "1986-10554", journalabbrev = "Parallel Comput.", jrldate = "Oct. 1986", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{FernandezVelicia:1986:HPA, author = "F. J. {Fern{\'a}ndez Velicia}", title = "High-precision analytic approximations for the {Fermi-Dirac} functions by means of elementary functions", journal = "Phys. Rev. A (3)", volume = "34", number = "5", pages = "4387--4395", year = "1986", CODEN = "PLRAAN", ISSN = "1050-2947", MRclass = "33A70 (82A05)", MRnumber = "MR869021 (88b:33024)", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Physical Review. A. Third Series", } @InProceedings{Gal:1986:CEF, author = "Shmuel Gal", title = "Computing elementary functions: a new approach for achieving high accuracy and good performance", crossref = "Miranker:1986:ASC", pages = "1--16", year = "1986", MRclass = "65D20", MRnumber = "868 283", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz", acknowledgement = ack-nhfb, } @InProceedings{Gustavson:1986:FEF, author = "F. G. Gustavson", title = "Fast Elementary Function Algorithms for 370 Machines", crossref = "Miranker:1986:ASC", pages = "17--17", year = "1986", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz", acknowledgement = ack-nhfb, } @Article{Hull:1986:VPE, author = "T. E. Hull and A. Abrham", title = "Variable Precision Exponential Function", journal = j-TOMS, volume = "12", number = "2", pages = "79--91", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15 (65D20)", MRnumber = "863 786", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/6498.html; http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/", acknowledgement = ack-nhfb, bibno = "91", content = "algorithms; verification; THEORY", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Algorithm analysis; G.4 Certification and testing; G.4 Verification", CRnumber = "1986-02428", descriptor = "mathematics of computing, numerical analysis, approximation, elementary function approximation; mathematics of computing, mathematical software, algorithm analysis; mathematics of computing, mathematical software, certification and testing; mathematics of computing, mathematical software, verification", fortitle = "ACM Trans. Math. Softw.", genterm = "June 1986", guideno = "2", keywords = "algorithms; theory; verification", review = "ACM CR 8702-0091", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification.", waffil = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE", } @Article{Muller:1986:MDC, author = "Jean-Michel Muller", title = "Une m{\'e}thodologie du calcul hardware des fonctions {\'e}l{\'e}mentaires. ({French}) [{A} methodology for the hardware computation of elementary functions]", journal = j-MATH-MODEL-NUM-ANA, volume = "20", number = "4", pages = "667--695", year = "1986", CODEN = "RMMAEV", ISSN = "0764-583X", MRclass = "65D20 (41-04)", MRnumber = "88h:65043", MRreviewer = "E. W. Cheney", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Reichel:1986:PAU, author = "L. Reichel", title = "On polynomial approximation in the uniform norm by the discrete least squares method", journal = j-BIT, volume = "26", number = "3", pages = "350--368", month = jan, year = "1986", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "12404", catcode = "G.1.2; G.1.2; G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Least squares approximation; G.1.2 Approximation; G.1.2 Spline and piecewise polynomial approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation", genterm = "algorithms", guideno = "1986-03278", jrldate = "Jan. 1986", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{S:1986:CEF, author = "A. S. Kuz'menko and K. I. Rogozin", title = "Calculation of elementary functions in a number system with arbitrary basis on the basis of order-differential transformations. ({Russian})", journal = "Prace Nauk. Inst. Cybernet. Tech. Politech. Wroc{\l}aw. Ser. Konfer.", volume = "74", number = "31", pages = "259--262", year = "1986", MRclass = "65G99 (65D20)", MRnumber = "894 691", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Shore:1986:AID, author = "Haim Shore", title = "An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres", journal = j-J-STAT-COMPUT-SIMUL, volume = "23", number = "3", pages = "157--181", year = "1986", CODEN = "JSCSAJ", ISSN = "0094-9655", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Ban-llan University, Israel", bibno = "5358", catcode = "G.3; G.m; G.1.2; G.2.1; J.3; G.3", content = "The author worked on a project to predict the percentage of time that operations are carried out relative to the time that the operating theater is available. The numerator of the percentage is a weighted sum of the times required to carry out different kinds of operations, where the weights are the numbers of operations of each kind to be performed. Since different kinds of operations have different mean times, this sum has a skewed distribution.\par Based on the Central Limit Theorem, the normal distribution is the most widely used approximation to the distribution of a weighted sum of random variables. However, this approximation is not very good if the sum has a skewed distribution.\par In a separate paper [1], the author derived an alternative approximation based on the first four moments of the sum. In the present paper, he applies this approximation to the operating theater problem by estimating the moments of the times of the different kinds of operations. The paper also contains a Monte Carlo comparison of the normal approximation with the proposed approximation for four underlying distributions of the sum.", CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2 Elementary function approximation; G.2.1 Combinatorics; G.2.1 Generating functions; J.3 Health; G.3 Probabilistic algorithms (including Monte Carlo)", CRnumber = "8612-1109", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, MISCELLANEOUS; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Generating functions; Computer Applications, LIFE AND MEDICAL SCIENCES, Health; Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo)", genterm = "algorithms; measurement", journalabbrev = "J. Stat. Comput. Simul.", jrldate = "1986", reviewer = "M. Snyder", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.m MISCELLANEOUS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; J. Computer Applications; J.3 LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS", } @Article{Skeel:1986:CVS, author = "Robert D. Skeel", title = "Construction of Variable-Stepsize Multistep Formulas", journal = j-MATH-COMPUT, volume = "47", number = "176", pages = "503--510, S45--S52", month = oct, year = "1986", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65L05", MRnumber = "87j:65080", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4110 (Error analysis in numerical methods); C4170 (Differential equations)", corpsource = "Dept. of Comput. Sci., Illnois Univ., Urbana, IL, USA", keywords = "Adams formula; adaptable multistep methods; backward-differentiation; differential equations; error analysis; estimation; first Dahlquist barrier; fixed leading coefficient method; fixed-coefficient methods; fixed-stepsize; formula; formula changing; initial value; interpolatory methods; local error; minimum storage variable-stepsize; multistep formula; Nordsieck stepsize changing technique; problems; step methods; variable; variable coefficient methods; variable-order family of variable-coefficient formulas", treatment = "T Theoretical or Mathematical", } @Article{Skeel:1986:SCV, author = "Robert D. Skeel", title = "Supplement to Construction of Variable-Stepsize Multistep Formulas", journal = j-MATH-COMPUT, volume = "47", number = "176", pages = "S45--S52", month = oct, year = "1986", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Temme:1986:DIC, author = "N. M. Temme", title = "A double integral containing the modified {Bessel} function: asymptotics and computation", journal = j-MATH-COMPUT, volume = "47", number = "176", pages = "683--691", month = oct, year = "1986", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33A40 (41A60 65D30)", MRnumber = "87m:33006", MRreviewer = "S. D. Bajpai", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Centre for Math. and Comput. Sci., Amsterdam, Netherlands", keywords = "distribution function; double integral; error analysis; error function; integral; integration; modified Bessel function; normal; polynomials; probability; series (mathematics); series expansions; two-dimensional", treatment = "T Theoretical or Mathematical", } @Article{Zaritskaya:1986:ACE, author = "Z. V. Zaritskaya and A. I. Shva{\u{\i}} and P. \=E. Antonyuk", title = "Approximation of certain elementary functions in the metric ${L}$. ({Russian})", journal = "Vestnik L'vov. Politekhn. Inst.", volume = "202", pages = "38--40", year = "1986", MRclass = "149.41A10 (33A10)", MRnumber = "87j:41030", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Agarwal:1987:CNS, author = "Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman", title = "Clarification: {``New scalar and vector elementary functions for the IBM System/370''} [{IBM J. Res. Develop. {\bf 30} (1986), no. 2, 126--144}]", journal = j-IBM-JRD, volume = "31", number = "2", pages = "274--274", year = "1987", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "76W05", MRnumber = "MR894626", bibdate = "Wed Apr 13 06:46:35 2005", note = "See \cite{Agarwal:1986:NSV}.", acknowledgement = ack-nhfb, fjournal = "International Business Machines Corporation. Journal of Research and Development", } @PhdThesis{Braune:1987:HSF, author = "K. Braune", title = "{Hochgenaue Standardfunktionen f{\"u}r reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern} \toenglish {High-Accuracy Elementary Functions for Real and Complex Points and Intervals in Arbitrary Floating-Point Systems} \endtoenglish", type = "Dissertation", school = "Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1987", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Crandall:1987:EFE, author = "R. E. Crandall and J. P. Buhler", title = "Elementary function expansions for {Madelung} constants", journal = j-J-PHYS-A, volume = "20", number = "16", pages = "5497--5510", year = "1987", CODEN = "JPHAC5", ISSN = "0305-4470", MRclass = "82A60 (82-08)", MRnumber = "MR924725 (88m:82034)", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. A. Mathematical and General", } @Article{Dunham:1987:PMAa, author = "Charles B. Dunham", title = "Provably monotone approximations", journal = j-SIGNUM, volume = "22", number = "2", pages = "6--11", month = apr, year = "1987", CODEN = "SNEWD6", DOI = "http://doi.acm.org/10.1145/24936.24938", ISSN = "0163-5778", bibdate = "Tue Apr 12 07:50:15 MDT 2005", bibsource = "http://portal.acm.org/", acknowledgement = ack-nhfb, keywords = "theory; verification", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation", } @Article{Dunham:1987:PMAb, author = "Charles B. Dunham", title = "Provably monotone approximations, {II}", journal = j-SIGNUM, volume = "22", number = "3", pages = "30--31", month = jul, year = "1987", CODEN = "SNEWD6", DOI = "http://doi.acm.org/10.1145/36318.36323", ISSN = "0163-5778", bibdate = "Tue Apr 12 07:50:15 MDT 2005", bibsource = "http://portal.acm.org/", acknowledgement = ack-nhfb, keywords = "theory", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation", } @Article{Gervais:1987:RAF, author = "R. Gervais and Q. I. Rahman and G. Schmeisser", title = "Representation and approximation of functions via $(0,2)$-interpolation", journal = j-J-APPROX-THEORY, volume = "50", number = "2", pages = "89--110", month = jun, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30719", catcode = "G.1.2; G.1.1", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.1 Interpolation; G.1.1 Spline and piecewise polynomial interpolation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation", genterm = "theory; verification", guideno = "1987-09238", journalabbrev = "J. Approx. Theory", jrldate = "June 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Kahan:1987:BCC, author = "W. Kahan", title = "Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit", crossref = "Iserles:1987:SAN", volume = "9", pages = "165--211", year = "1987", MRclass = "65E05", MRnumber = "88k:65027", bibdate = "Sat Jan 11 17:44:01 MST 1997", series = "Inst. Math. Appl. Conf. Ser. New Ser.", acknowledgement = ack-nhfb, } @PhdThesis{Kramer:1987:ISR, author = "W. Kr{\"a}mer", title = "Inverse Standardfunktionen f{\"u}r reelle und komplexe Intervallargumente mit a priori Fehlerabsch{\"a}tzungen f{\"u}r beliebige Datenformate \toenglish {Inverse Elementary Functions for Real and Complex Interval Arguments with {A}-Priori Error Estimates for Arbitrary Data Formats} \endtoenglish", type = "Dissertation", school = "Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1987", bibdate = "Fri Sep 16 16:30:41 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @MastersThesis{Liu:1987:BEF, author = "Z. A. Liu", title = "{Berkeley} Elementary Function Test Suite", type = "{M.S.} thesis", school = "Computer Science Division, Department of Electrical Engineering and Computer Science, Univerity of California at Berkeley", address = "Berkeley, CA, USA", month = dec, year = "1987", bibdate = "Mon Sep 12 23:52:34 1994", acknowledgement = ack-nj, } @InProceedings{Mathis:1987:EFP, author = "Robert F. Mathis", title = "Elementary Functions Package for {Ada}", crossref = "ACM:1987:UAA", pages = "95--100", month = dec, year = "1987", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz", acknowledgement = ack-nhfb, } @Article{Moricz:1987:ACF, author = "Ferenc Moricz and Xianliang Shi", title = "Approximation to continuous functions by {Cesaro} means of double {Fourier} series and conjugate series", journal = j-J-APPROX-THEORY, volume = "49", number = "4", pages = "346--377", month = apr, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30744", catcode = "G.1.2; G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Least squares approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation", genterm = "theory; verification", guideno = "1987-09224", journalabbrev = "J. Approx. Theory", jrldate = "April 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Musielak:1987:AEG, author = "J. Musielak", title = "Approximation of elements of a generalized {Orlicz} sequence space by nonlinear, singular kernels", journal = j-J-APPROX-THEORY, volume = "50", number = "4", pages = "366--372", month = aug, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30716", catcode = "G.2.1; G.1.5; G.1.2", CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5 Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Generating functions; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1987-09257", journalabbrev = "J. Approx. Theory", jrldate = "Aug. 1987", subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Pereira:1987:CEC, author = "N. Costa Pereira", title = "Corrigendum: {``Estimates for the {Chebyshev} function $\psi(x)-\theta(x)$''} {[Math. Comp. {\bf 44} (1985), no. 169, 211--221, MR 86k:11005]}", journal = j-MATH-COMPUT, volume = "48", number = "177", pages = "447--447", month = jan, year = "1987", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "11A25 (11N45 11Y35 33A70)", MRnumber = "87k:11006", bibdate = "Thu Jun 15 07:27:03 2000", note = "See \cite{Pereira:1985:ECF}.", acknowledgement = ack-nhfb, } @Article{Proinov:1987:NIA, author = "Petko D. Proinov", title = "Numerical integration and approximation of differentiable functions, {II}", journal = j-J-APPROX-THEORY, volume = "50", number = "4", pages = "373--393", month = aug, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30717", catcode = "G.1.4; G.1.2", CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1987-09258", journalabbrev = "J. Approx. Theory", jrldate = "Aug. 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Smith:1987:BAM, author = "P. W. Smith and J. J. Swetits", title = "Best approximation by monotone functions", journal = j-J-APPROX-THEORY, volume = "49", number = "4", pages = "398--403", month = apr, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30747", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1987-09227", journalabbrev = "J. Approx. Theory", jrldate = "April 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Book{Spanier:1987:AF, author = "Jerome Spanier and Keith B. Oldham", title = "An Atlas of Functions", publisher = "Hemisphere Publishing Corporation", address = "Washington, DC, USA", pages = "ix + 700", year = "1987", ISBN = "0-89116-573-8, 3-540-17395-1", ISBN-13 = "978-0-89116-573-6, 978-3-540-17395-3", LCCN = "QA331 .S685 1987", bibdate = "Fri Aug 31 16:20:13 MDT 2007", bibsource = "z3950.loc.gov:7090/Voyager", price = "US\$90.00 (est.)", acknowledgement = ack-nhfb, subject = "elementary functions; special functions; cognate functions; complementary incomplete gamma function; complementary modulus; complete beta function; complex argument when; cosecant functions; cotangent functions; digamma function; economized polynomial; error function complement; eta numbers; function and its reciprocal; hypergeometric algorithm; important definite integrals; incomplete elliptic integrals; inverse gudermannian function; inverse hyperbolic functions; negative integer order; other definite integrals; parabolic cylinder function; polygamma functions; purely imaginary argument; reciprocal linear function; reflection formula", } @Article{Stoyanov:1987:AE, author = "Basil J. Stoyanov and Richard A. Farrell", title = "On the Asymptotic Evaluation of $\int^{\pi/2}_0 {J}^2_0(\gamma \sin x) dx$", journal = j-MATH-COMPUT, volume = "49", number = "179", pages = "275--279", month = jul, year = "1987", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "41A60 (65D30)", MRnumber = "88e:41067", MRreviewer = "Roderick Wong", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Analysis); C4180 (Integral equations)", corpsource = "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA", keywords = "analytical expression; asymptotic behavior; asymptotic evaluation; Bessel functions; first kind; integral; integral equations; order Bessel function; positive parameter; zeroth-", treatment = "T Theoretical or Mathematical", } @InProceedings{Tanese:1987:PGA, author = "Reiko Tanese", editor = "John J. Grefenstette", booktitle = "Genetic algorithms and their applications: proceedings of the second International Conference on Genetic Algorithms: July 28--31, 1987 at the Massachusetts Institute of Technology, Cambridge, MA", title = "Parallel genetic algorithms for a hypercube", publisher = "Lawrence Erlbaum Associates, Inc.", address = "Hillsdale, NJ, USA", pages = "177--183", year = "1987", ISBN = "0-8058-0158-8, 0-8058-0159-6 (paperback)", ISBN-13 = "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)", LCCN = "Q334 .I5561 1987", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", price = "US\$39.95", acknowledgement = ack-nhfb, bibno = "42536", bookpages = "260", catcode = "I.2.6; G.1.0; G.1.2; C.1.2", CRclass = "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0 Parallel algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; C.1.2 Multiple Data Stream Architectures (Multiprocessors); C.1.2 Parallel processors", descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE, Learning, Analogies; Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Parallel processors", genterm = "algorithms; performance; experimentation", guideno = "1988-16888", procdate = "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and Bolt Beranek & Newman, July 28-31, 1987", procloc = "Cambridge, MA", subject = "I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES", } @Article{Thompson:1987:IEF, author = "Peter Thompson", title = "Implementing an Elementary Function Library", journal = j-SIGNUM, volume = "22", number = "2", pages = "2--5", month = apr, year = "1987", CODEN = "SNEWD6", ISSN = "0163-5778", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991); garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb # " and " # ack-nj, bibno = "24937", catcode = "G.m; D.3.2", CRclass = "D.3.2 Language Classifications; D.3.2 OCCAM", descriptor = "Mathematics of Computing, MISCELLANEOUS; Software, PROGRAMMING LANGUAGES, Language Classifications, OCCAM", genterm = "theory; languages", guideno = "1987-03363", journalabbrev = "SIGNUM Newsl.", jrldate = "April 1987", subject = "G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.3 PROGRAMMING LANGUAGES", } @Article{Timan:1987:DFP, author = "A. F. Timan", title = "Distribution of fractional parts and approximation of functions with singularities by {Bernstein} polynomials", journal = j-J-APPROX-THEORY, volume = "50", number = "2", pages = "167--174", month = jun, year = "1987", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "30725", catcode = "G.1.5; G.1.2", CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials, methods for; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1987-09244", journalabbrev = "J. Approx. Theory", jrldate = "June 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Zwick:1987:BAC, author = "D. Zwick", title = "Best approximation by convex functions", journal = j-AMER-MATH-MONTHLY, volume = "94", number = "6", pages = "528--534", month = jul, year = "1987", CODEN = "AMMYAE", ISSN = "0002-9890", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "University of Vermont, Vermont, NY", bibno = "43727", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1988-04405", journalabbrev = "Am. Math. Monthly", jrldate = "June/July 1987", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Book{Aberth:1988:PNA, author = "Oliver Aberth", title = "Precise Numerical Analysis", publisher = pub-WCB, address = pub-WCB:adr, pages = "x + 225", year = "1988", ISBN = "0-697-06760-2", ISBN-13 = "978-0-697-06760-9", LCCN = "QA297 .A28 1988", bibsource = "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib", abstract = "Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $\pm$ a range. Rational arithmetic is also considered. Chapters are devoted to \begin{enumerate} \item rootfinding, \item polynomial rootfinding, \item numerical linear algebra, \item differentiation and integration, and \item ordinary differential equations.\end{enumerate} Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an {\it a priori\/} bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.", acknowledgement = ack-nj, comment = "Text for a one semester, junior level course in numerical analysis. Includes PC disk with software written in PBASIC. Sound introductory level discussion of code lists and error capture techniques.", keywords = "general numerical analysis; interval techniques; differentiation arithmetic; variable precision arithmetic; linear algebra; differentiation; integration; ordinary differential equations.", } @Article{Alonso:1988:SCN, author = "Javier Alonso and Carlos Benitez", title = "Some characteristic and non-characteristic properties of inner product spaces", journal = j-J-APPROX-THEORY, volume = "55", number = "3", pages = "318--325", month = dec, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56052", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; verification", guideno = "1988-10198", journalabbrev = "J. Approx. Theory", jrldate = "Dec. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Bloom:1988:LCL, author = "Thomas Bloom", title = "The {Lebesgue} constant for {Lagrange} interpolation in the simplex", journal = j-J-APPROX-THEORY, volume = "54", number = "3", pages = "338--353", month = sep, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56887", catcode = "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7", CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems", guideno = "1988-10170", journalabbrev = "J. Approx. Theory", jrldate = "Sept. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Borwein:1988:CFF, author = "J. M. Borwein and P. B. Borwein", title = "On the complexity of familiar functions and numbers", journal = j-SIAM-REVIEW, volume = "30", number = "4", pages = "589--601", month = dec, year = "1988", CODEN = "SIREAD", ISSN = "0036-1445", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "58008", catcode = "G.1.2; F.2.1; F.1.3", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.1.3 Complexity Classes", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes", genterm = "algorithms; theory; performance", guideno = "1988-13907", journalabbrev = "SIAM Rev.", jrldate = "Dec. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES", } @Article{Borwein:1988:PAE, author = "Peter B. Borwein", title = "Pad{\'e} approximants for the $q$-elementary functions", journal = j-CONST-APPROX, volume = "4", number = "4", pages = "391--402", year = "1988", ISSN = "0176-4276", MRclass = "41A21 (33A10 41A20)", MRnumber = "89f:41022", MRreviewer = "Annie A. M. Cuyt", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Cartwright:1988:JTC, author = "Donald I. Cartwright and Krzysztof Kucharski", title = "{Jackson's Theorem} for compact connect {Lie} groups", journal = j-J-APPROX-THEORY, volume = "55", number = "3", pages = "352--359", month = dec, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56056", catcode = "G.2.m; G.1.2", CRclass = "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1988-10202", journalabbrev = "J. Approx. Theory", jrldate = "Dec. 1988", subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Cover:1988:DII, author = "Thomas M. Cover and Joy A. Thomas", title = "Determinant inequalities via information theory", journal = j-SIAM-J-MAT-ANA-APPL, volume = "9", number = "3", pages = "384--392", month = jul, year = "1988", CODEN = "SJMAEL", ISSN = "0895-4798", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "58040", catcode = "H.1.1; G.1.3; F.2.1; G.1.2", CRclass = "H.1.1 Systems and Information Theory; H.1.1 Information theory; G.1.3 Numerical Linear Algebra; G.1.3 Determinants; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Information Systems, MODELS AND PRINCIPLES, Systems and Information Theory, Information theory; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Determinants; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; performance", guideno = "1988-13777", journalabbrev = "SIAM J. Matrix Anal. Appl.", jrldate = "July 1988", subject = "H. Information Systems; H.1 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Davenport:1988:ICF, author = "J. H. Davenport", editor = "N. M. Stephens and M. P. Thorne", booktitle = "Computers in mathematical research: based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on computers in mathematical research, held at University College, Cardiff in September 1986", title = "Integration in closed form", volume = "14", publisher = pub-CLARENDON-PRESS, address = pub-CLARENDON-PRESS:adr, year = "1988", ISBN = "0-19-853620-8", ISBN-13 = "978-0-19-853620-8", LCCN = "QA11.A1 C618 1986", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", price = "US\$57.50", series = "Institute of Mathematics and its applications conference series, new series", acknowledgement = ack-nhfb, affiliation = "Univ. of Bath", bibno = "52474", bookpages = "235", catcode = "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1", CRclass = "J.2 Mathematics and statistics; F.2.1 Numerical Algorithms and Problems; F.2.1 Number-theoretic computations; G.1.2 Approximation; G.1.2 Rational approximation; G.1.2 Approximation; G.1.2 Elementary function approximation; I.2.9 Robotics; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations in finite fields", descriptor = "Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Computing Methodologies, ARTIFICIAL INTELLIGENCE, Robotics; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields", genterm = "algorithms; theory", guideno = "1988-16247", page = "119--134", procdate = "Sept. 1986", procloc = "Cardiff, Wales", subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", waffil = "Univ. College, Cardiff, Wales; Univ. College, Cardiff, Wales", } @Article{Dunham:1988:PMA, author = "Charles B. Dunham", title = "Provably monotone approximations, {III}", journal = j-SIGNUM, volume = "23", number = "1", pages = "10--10", month = jan, year = "1988", CODEN = "SNEWD6", DOI = "http://doi.acm.org/10.1145/43931.43934", ISSN = "0163-5778", bibdate = "Tue Apr 12 07:50:16 MDT 2005", bibsource = "http://portal.acm.org/", acknowledgement = ack-nhfb, keywords = "theory", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation", } @TechReport{Duprat:1988:EPE, author = "J. Duprat and J. M. Muller", title = "Evaluation of Polynomials and elementary Functions by integrated Circuits", number = "RR698-I", institution = "IMAG", address = "Grenoble, France", month = jan, year = "1988", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz", acknowledgement = ack-nhfb, } @Article{Duprat:1988:HPE, author = "Jean Duprat and Jean-Michel Muller", title = "Hardwired polynomial evaluation", journal = j-J-PAR-DIST-COMP, volume = "5", number = "3", pages = "291--309", month = jun, year = "1988", CODEN = "JPDCER", ISSN = "0743-7315", bibdate = "Sat Apr 12 19:06:31 MDT 1997", bibsource = "Compendex database", acknowledgement = ack-nhfb, affiliationaddress = "CNRS, Grenoble, Fr", classification = "721; 722; 723; 921; C4130 (Interpolation and function approximation); C5230 (Digital arithmetic methods)", corpsource = "Inst. Nat. Polytech. de Grenoble, France", journalabr = "J Parallel Distrib Comput", keywords = "computer architecture; computers, digital --- Circuits; digital arithmetic; elementary functions; hardwired polynomial evaluation; mathematical functions; mathematical techniques; Polynomials; polynomials; special-purpose circuits; VLSI implementation; VLSI implementation", treatment = "P Practical", } @Article{Feng:1988:AIN, author = "Y. Y. Feng and J. Kozak", title = "An approach to the interpolation of nonuniformly spaced data", journal = j-J-COMP-APPL-MATH, volume = "23", number = "2", pages = "169--178", month = aug, year = "1988", CODEN = "JCAMDI", ISSN = "0377-0427", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56475", catcode = "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4", CRclass = "G.1.1 Interpolation; G.1.1 Spline and piecewise polynomial interpolation; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems; G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature and Numerical Differentiation; G.1.4 Error analysis", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing; Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Error analysis", genterm = "algorithms; theory", guideno = "1988-10490", journalabbrev = "J. Comput. Appl. Math.", jrldate = "August 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Gawronski:1988:ZLT, author = "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller", title = "On the zeros of {Lerch}'s transcendental function of real parameters", journal = j-J-APPROX-THEORY, volume = "53", number = "3", pages = "354--364", month = jun, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG", bibno = "49727", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1988-10146", journalabbrev = "J. Approx. Theory", jrldate = "June 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Heilmann:1988:SSM, author = "Margareta Heilmann", title = "{$L_p$}-saturation of some modified {Bernstein} operators", journal = j-J-APPROX-THEORY, volume = "54", number = "3", pages = "260--273", month = sep, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56880", catcode = "G.1.2; G.1.9; G.1.7; G.1.7", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.9 Integral Equations; G.1.9 Integro-differential equations; G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability", genterm = "algorithms; theory", guideno = "1988-10163", journalabbrev = "J. Approx. Theory", jrldate = "Sept. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Horwitz:1988:TPF, author = "Alan L. Horwitz and Lee A. Rubel", title = "Totally positive functions and totally bounded functions on $[-1,1]$", journal = j-J-APPROX-THEORY, volume = "52", number = "2", pages = "204--216", month = feb, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Pennsylvania State Univ., University Park; Univ. of Illinois, Urbana", bibno = "49653", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1988-10106", journalabbrev = "J. Approx. Theory", jrldate = "February 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Johnsson:1988:DPP, author = "S. L. Johnsson", editor = "J. R. Rice", booktitle = "Mathematical aspects of scientific software", title = "Data parallel programming and basic linear algebra subroutines", volume = "14", publisher = pub-SV, address = pub-SV:adr, pages = "183--196", year = "1988", ISBN = "0-387-96706-0", ISBN-13 = "978-0-387-96706-6", LCCN = "QA76.76.D47 M366 1988", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", series = "The IMS volumes in mathematics and its applications", acknowledgement = ack-nhfb, bibno = "42725", bookpages = "vi + 208", catcode = "G.1.2; D.1.m; G.4", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; D.1.m Miscellaneous", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Software, PROGRAMMING TECHNIQUES, Miscellaneous; Mathematics of Computing, MATHEMATICAL SOFTWARE", genterm = "theory; algorithms; design; languages", guideno = "1988-02324", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE", waffil = "Purdue Univ., West Lafayette, IN", } @Article{Kowalski:1988:ASP, author = "Marek Kowalski and Waldemar Sielski", title = "Approximation of smooth periodic functions in several variables", journal = j-J-COMPLEXITY, volume = "4", number = "4", pages = "356--372", month = dec, year = "1988", CODEN = "JOCOEH", ISSN = "0885-064X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56811", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; verification; theory", guideno = "1988-10411", journalabbrev = "J. Complexity", jrldate = "Dec. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Kramer:1988:ISF, author = "W. Kramer", title = "Inverse standard functions for real and complex point and interval arguments with dynamic accuracy", journal = j-COMPUTING-SUPPLEMENTUM, pages = "185--212", year = "1988", CODEN = "COSPDM", ISSN = "0344-8029", bibdate = "Thu Dec 14 17:19:38 MST 1995", note = "Computer Arithmetic and Scientific Computation.", abstract = "Algorithms to compute inverse standard functions to arbitrary accuracy with safe error bounds are given. Not only approximation errors but also all possible rounding errors are considered. The desired accuracy of the function as well as the base of the number system used are parameters of the error formula. For implementation it is only assumed that the four elementary arithmetic operations are performed with a certain number of correct digits of the function value. The interval routines are constructed out of the point routines considering the monotonicity behaviour of the functions. The ambiguity of the complex functions is briefly discussed.", acknowledgement = ack-nhfb, affiliation = "Karlsruhe Univ., West Germany", classification = "B0290F (Interpolation and function approximation); B0290B (Error analysis in numerical methods); C4130 (Interpolation and function approximation); C4110 (Error analysis in numerical methods)", confdate = "30 Sept.-2 Oct. 1987", conflocation = "Karlsruhe, West Germany", confsponsor = "Karlsruhe Univ.; GAMM Committee", issue = "no.6 p. 185-212", keywords = "Interval arguments; Dynamic accuracy; Inverse standard functions; Approximation errors; Rounding errors; Error formula; Monotonicity behaviour", language = "English", pubcountry = "Austria", thesaurus = "Error analysis; Function approximation", } @Article{Lou:1988:ETR, author = "Lou van den Dries", title = "On the elementary theory of restricted elementary functions", journal = j-J-SYMBOLIC-LOGIC, volume = "53", number = "3", pages = "796--808", year = "1988", CODEN = "JSYLA6", ISSN = "0022-4812", MRclass = "03C65 (03C40 03C68 12L12)", MRnumber = "89i:03074", MRreviewer = "M. Yasuhara", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Mimachi:1988:PRI, author = "Katsuhisa Mimachi", title = "A proof of {Ramanujan}'s identity by use of loop integrals", journal = j-SIAM-J-MATH-ANA, volume = "19", number = "6", pages = "1490--1493", month = nov, year = "1988", CODEN = "SJMAAH", ISSN = "0036-1410", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "58904", catcode = "G.1.9; G.1.2; F.2.2", CRclass = "G.1.9 Integral Equations; G.1.9 Integro-differential equations; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations", genterm = "algorithms; theory", guideno = "1988-13744", journalabbrev = "SIAM J. Math. Anal.", jrldate = "Nov. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @Article{Olver:1988:EBL, author = "F. W. J. Olver", title = "Error Bounds for Linear Recurrence Relations", journal = j-MATH-COMPUT, volume = "50", number = "182", pages = "481--499", month = apr, year = "1988", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65Q05 (39A10 65G05)", MRnumber = "89e:65146", MRreviewer = "B. Choczewski", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290B (Error analysis in numerical methods); C4110 (Error analysis in numerical methods)", corpsource = "Maryland Univ., College Park, MD, USA", keywords = "a posteriori methods; analysis; Bessel function; bounds; computational complexity; difference equations; error; homogeneous second order; Legendre function; linear recurrence relations; monotonic systems; numerical examples; O(r) arithmetic operations; oscillatory systems; realistic error; relations; rounded interval arithmetic", treatment = "T Theoretical or Mathematical", } @Article{Polyak:1988:SOM, author = "R. A. Polyak", title = "Smooth optimization methods for minimax problems", journal = j-SIAM-J-CONTROL-OPTIM, volume = "26", number = "6", pages = "1274--1286", month = nov, year = "1988", CODEN = "SJCODC", ISSN = "0363-0129", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "57989", catcode = "G.1.6; G.1.2; F.2.1; G.1.2", CRclass = "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; performance", guideno = "1988-13621", journalabbrev = "SIAM J. Control Optim.", jrldate = "Nov. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InCollection{Powell:1988:RBF, author = "J. D. Powell", editor = "D. F. (David Francis) Griffiths and G. A. Watson", booktitle = "Numerical analysis 1987", title = "Radial basis function approximations to polynomials", volume = "170", publisher = "Longman, Inc.", address = "New York, NY, USA", pages = "223--241", year = "1988", ISBN = "0-582-02157-X", ISBN-13 = "978-0-582-02157-0", LCCN = "QA297.N828 1988", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", price = "US\$54.95", series = "Pitman research notes in mathematics series", acknowledgement = ack-nhfb, bibno = "54996", bookpages = "300", catcode = "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Spline and piecewise polynomial approximation; G.1.9 Integral Equations; G.1.9 Integro-differential equations; G.1.1 Interpolation; G.1.1 Spline and piecewise polynomial interpolation; G.3 Statistical computing; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability", genterm = "algorithms; performance", guideno = "1988-01246", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", waffil = "Univ. of Dundee; Univ. of Dundee", } @Article{Proinov:1988:ISF, author = "Petko D. Proinov", title = "Integration of smooth functions and $\phi$-discrepancy", journal = j-J-APPROX-THEORY, volume = "52", number = "3", pages = "284--292", month = mar, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Plovdiv, Plovdiv, Bulgaria", bibno = "49659", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1988-10111", journalabbrev = "J. Approx. Theory", jrldate = "March 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Richardson:1988:NMT, author = "Daniel Richardson", title = "Nonstandard models of the theory of elementary functions of a real variable", journal = j-Z-MATH-LOGIK-GRUNDL-MATH, volume = "34", number = "4", pages = "355--372", year = "1988", CODEN = "ZMLGAQ", ISBN = "0044-3050", ISBN-13 = "0044-3050", ISSN = "0044-3050", MRclass = "03B30 (03C62 03H15 26E35)", MRnumber = "90a:03009", MRreviewer = "Reuven H. Gurevi{\v{c}}", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Ruscheweyh:1988:EST, author = "Stephan Ruscheweyh", title = "Extension of {Szeg{\H{o}}}'s theorem on the sections of univalent functions", journal = j-SIAM-J-MATH-ANA, volume = "19", number = "6", pages = "1442--1449", month = nov, year = "1988", CODEN = "SJMAAH", ISSN = "0036-1410", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "58899", catcode = "G.1.2; G.1.9; F.2.2; F.2.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.9 Integral Equations; G.1.9 Integro-differential equations; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Computations on discrete structures; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations", genterm = "algorithms; theory", guideno = "1988-13739", journalabbrev = "SIAM J. Math. Anal.", jrldate = "Nov. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @InProceedings{Schwarz:1988:CLI, author = "Jerry Schwarz", title = "A {C++} Library for Infinite Precision Floating Point", crossref = "USENIX:1988:UPC", pages = "271--281", year = "1988", bibdate = "Tue Dec 12 09:20:21 MST 1995", bibsource = "ftp://ftp.uu.net/library/bibliography", abstract = "The Real library supports infinite precision floating point computation in C++. Arbitrary precision rational arithmetic and transcendental functions are supported.", acknowledgement = ack-nhfb, affiliation = "AT\&T Bell Laboratories, Murray Hill", bookpages = "362", classification = "C6130 (Data handling techniques); C5230 (Digital arithmetic methods)", confdate = "17--21 Oct. 1988", conflocation = "Denver, CO, USA", keywords = "C++ library; Infinite precision floating point; Real library; Rational arithmetic; Transcendental functions", language = "English", pubcountry = "USA", thesaurus = "C language; Digital arithmetic; Object-oriented programming; Subroutines", } @InProceedings{Sobczyk:1988:SMA, author = "Kazimierz Sobczyk", editor = "W. Schiehlen and W. Wedig", booktitle = "Analysis and estimation of stochastic mechanical systems", title = "Stochastic modelling and analysis of fatigue", volume = "303", publisher = pub-SV, address = pub-SV:adr, pages = "269--313", year = "1988", ISBN = "0-387-82058-2", ISBN-13 = "978-0-387-82058-3", LCCN = "TA350.3.I5 no.303; TJ173 .A531 1988", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", series = "Courses and lectures", acknowledgement = ack-nhfb, bibno = "58064", bookpages = "350", catcode = "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9", CRclass = "J.2 Engineering; I.6.3 Applications; G.1.8 Partial Differential Equations; G.1.8 Difference methods; G.3 Probabilistic algorithms (including Monte Carlo); G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.9 Integral Equations; G.1.9 Integro-differential equations", descriptor = "Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering; Computing Methodologies, SIMULATION AND MODELING, Applications; Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods; Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo); Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations", genterm = "algorithms; theory; design; measurement; reliability", guideno = "1988-17476", procdate = "1987", procloc = "International Centre for Mechanical Sciences in Udine", subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", waffil = "Univ. of Stuttgart; Univ. of Karlsruhe", } @Article{Stephens:1988:SCR, author = "A. J. Stephens and H. C. Williams", title = "Some computational results on a problem concerning powerful numbers", journal = j-MATH-COMPUT, volume = "50", number = "182", pages = "619--632", month = apr, year = "1988", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "11R11 (11A51 11R27 11Y16 11Y40)", MRnumber = "89d:11091", MRreviewer = "H. J. Godwin", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0210 (Algebra); B0250 (Combinatorial mathematics); C1110 (Algebra); C1160 (Combinatorial mathematics)", corpsource = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man., Canada", keywords = "computational complexity; continued; fractions; free integer; fundamental unit; number theory; positive square-; real quadratic number fields; regulator algorithm Amdahl 5850; step algorithm; time complexity $O(D^{1/4+\epsilon})$", treatment = "T Theoretical or Mathematical; X Experimental", } @InProceedings{Stillinger:1988:CPS, author = "Frank H. Stillinger", editor = "Donald G. Truhlar", booktitle = "Mathematical frontiers in computational chemical physics", title = "Collective phenomena in statistical mechanics and the geometry of potential energy hypersurfaces", volume = "15", publisher = pub-SV, address = pub-SV:adr, pages = "157--173", year = "1988", ISBN = "0-387-96782-6", ISBN-13 = "978-0-387-96782-0", LCCN = "QD455.3.M3 M38 1988", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", note = "Proceedings of the Workshop on Atomic and Molecular Structure and Dynamics, held June 15--July 24, 1987, at the Institute for Mathematics and Its Applications, University of Minnesota.", price = "US\$36.80", series = "The IMA volumes in mathematics and its applications", acknowledgement = ack-nhfb, bibno = "58051", bookpages = "xii + 349", catcode = "J.2; J.2; J.2; F.2.2; G.3; G.1.2", CRclass = "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; G.3 Statistical computing; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "1988-17776", procdate = "1982", procloc = "Univ. of Minnesota, Minneapolis", subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", waffil = "Univ. of Minnesota, Minneapolis", } @Article{Sun:1988:SAF, author = "Xiehua Sun", title = "On the simultaneous approximation of functions and their derivatives by the {Szasz-Mirakyan} operator", journal = j-J-APPROX-THEORY, volume = "55", number = "3", pages = "279--288", month = dec, year = "1988", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "56048", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1988-10194", journalabbrev = "J. Approx. Theory", jrldate = "Dec. 1988", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @TechReport{Tang:1988:PIG, author = "Ping Tak Peter Tang", title = "Portable Implementation of a Generic Exponential Function", type = "Technical report", number = "ANL-88-3", institution = inst-ANL, address = inst-ANL:adr, year = "1988", bibdate = "Fri Dec 28 11:27:51 2007", acknowledgement = ack-nhfb, } @Book{vanRijckevorsek:1988:CCA, editor = "Jan L. A. van Rijckevorsek and Jan de Leeus", title = "Component and correspondence analysis: dimension reduction by functional approximation", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiii + 146", year = "1988", ISBN = "0-471-91847-4", ISBN-13 = "978-0-471-91847-9", LCCN = "QA278.5 .C6571 1988", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", price = "US\$40", series = "Wiley series in probability and mathematical statistics", acknowledgement = ack-nhfb, bibno = "59092", catcode = "G.1.2; G.3", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.3 Statistical computing", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing", genterm = "theory; algorithms", guideno = "1988-03042", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS", } @Article{Wong:1988:AE, author = "R. Wong", title = "Asymptotic Expansion of $\int^{\pi/2}_0 {J}^2_\nu(\lambda \cos \theta) d\theta$", journal = j-MATH-COMPUT, volume = "50", number = "181", pages = "229--234", month = jan, year = "1988", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "41A60 (33A40)", MRnumber = "89g:41022", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "A0260 (Numerical approximation and analysis); A0270 (Computational techniques); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man., Canada", keywords = "asymptotic expansion; Bessel function; Bessel functions; crystallography; diffraction theory; function approximation; integral; integration", treatment = "T Theoretical or Mathematical", } @InProceedings{Ahmed:1989:EEF, author = "H. M. Ahmed", title = "Efficient Elementary Function Generation with Multipliers", crossref = "Ercegovac:1989:PSC", pages = "52--59", year = "1989", bibdate = "Sat Nov 27 14:19:10 MST 2004", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nhfb # " and " # ack-nj, } @Article{Armbruster:1989:KSD, author = "Dieter Armbruster and John Guckenheimer and Philip Holmes", title = "{Kuramoto-Sivashinsky} dynamics on the center-unstable manifold", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "676--691", month = jun, year = "1989", CODEN = "SMJMAP", ISSN = "0036-1399", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY", bibno = "64938", catcode = "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8", CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems; G.1.0 General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.8 Partial Differential Equations", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems; Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations", genterm = "algorithms; theory; experimentation", guideno = "1989-09707", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Avellaneda:1989:OBE, author = "Marco Avellaneda and Graeme W. Milton", title = "Optimal bounds on the effective bulk modulus of polycrystals", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "824--837", month = jun, year = "1989", CODEN = "SMJMAP", ISSN = "0036-1399", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64947", catcode = "G.1.8; J.2; G.1.2; G.1.6", CRclass = "G.1.8 Partial Differential Equations; G.1.8 Difference methods; J.2 Physics; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.6 Optimization; G.1.6 Constrained optimization", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization", genterm = "algorithms; theory; experimentation", guideno = "1989-09716", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Belaga:1989:TMM, author = "E. G. Belaga", title = "Through the mincing machine with a {Boolean} layer cake: nonstandard computations over {Boolean} circuits in the lower-bounds-to-circuit-size complexity proving", journal = j-ACTA-INFO, volume = "26", number = "4", pages = "381--407", month = feb, year = "1989", CODEN = "AINFA2", ISSN = "0001-5903", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. Louis Pasteur, Strasbourg Cedex, France and Univ. su Pisa, Pisa, Italy", bibno = "69310", catcode = "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2; F.2.2", CRclass = "F.4.1 Mathematical Logic; F.4.1 Computational logic; B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1 Models of Computation; F.1.1 Unbounded-action devices; F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Complexity of proof procedures; F.1.2 Modes of Computation; F.1.2 Alternation and nondeterminism; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Computations on discrete structures", descriptor = "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic; Hardware, LOGIC DESIGN, Design Styles, Combinational logic; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Unbounded-action devices; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Complexity of proof procedures; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Alternation and nondeterminism; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures", genterm = "algorithms; theory", guideno = "1989-03239", journalabbrev = "Acta Inf.", jrldate = "Feb. 1989", subject = "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @Article{Birge:1989:SUB, author = "John R. Birge and Roger J. Wets", title = "Sublinear upper bounds for stochastic programs with recourse", journal = j-MATH-PROG, volume = "43", number = "2", pages = "131--149", month = feb, year = "1989", CODEN = "MHPGA4", ISSN = "0025-5610", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Michigan, Ann Arbor; Univ. of California, Davis", bibno = "65226", catcode = "G.1.6; G.1.7; G.3; G.1.6; G.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; G.3 Probabilistic algorithms (including Monte Carlo); G.1.6 Optimization; G.1.6 Gradient methods; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo); Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; performance", guideno = "1989-09042", journalabbrev = "Math. Program.", jrldate = "February 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Borwein:1989:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", title = "{Ramanujan}, modular equations, and approximations to $\pi$ or how to compute one billion digits of $\pi$", journal = j-AMER-MATH-MONTHLY, volume = "96", number = "3", pages = "201--219", month = mar, year = "1989", CODEN = "AMMYAE", ISSN = "0002-9890", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Dalhouise Univ., Halifax; Dalhouise Univ., Halifax", bibno = "65243", catcode = "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1", CRclass = "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.8 Partial Differential Equations; G.1.8 Elliptic equations; G.1.4 Quadrature and Numerical Differentiation; G.1.4 Multiple quadrature; I.1.3 Languages and Systems; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms; F.2.1 Numerical Algorithms and Problems; F.2.1 Number-theoretic computations", descriptor = "Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations; Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature; Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations", genterm = "algorithms; theory", guideno = "1989-03459", journalabbrev = "Am. Math. Monthly", jrldate = "March 1989", subject = "I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @Article{Bos:1989:CPR, author = "L. Bos", title = "A characteristic of points in {$R^2$} having {Lebesgue} function of polynomial growth", journal = j-J-APPROX-THEORY, volume = "56", number = "3", pages = "316--329", month = mar, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72254", catcode = "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3", CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; G.1.1 Interpolation; G.1.1 Interpolation formulas; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; G.1.2 Approximation; G.1.2 Chebyshev approximation and theory; G.1.3 Numerical Linear Algebra; G.1.3 Sparse and very large systems", descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems", genterm = "algorithms; theory", guideno = "1989-07812", journalabbrev = "J. Approx. Theory", jrldate = "Mar. 1989", subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Bronstein:1989:AIE, author = "Manuel Bronstein", title = "An algorithm for the integration of elementary functions", journal = j-LECT-NOTES-COMP-SCI, volume = "378", pages = "491--497", year = "1989", CODEN = "LNCSD9", ISSN = "0302-9743", MRclass = "65D30", MRnumber = "91a:65050", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "EUROCAL '87 (Leipzig, 1987).", acknowledgement = ack-nhfb, } @InProceedings{Bronstein:1989:SRE, author = "M. Bronstein", title = "Simplification of real elementary functions", crossref = "ACM:1989:PAI", pages = "207--211", year = "1989", bibdate = "Tue Sep 17 06:46:18 MDT 1996", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author describes an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. He provides examples from its implementation in the Scratchpad computer algebra system that illustrate the advantages over the use of complex logarithms and exponentials.", acknowledgement = ack-nhfb, affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "Real elementary functions; Real structure theorem; Scratchpad; Computer algebra system", language = "English", thesaurus = "Functions; Mathematics computing; Symbol manipulation", } @Article{Cao:1989:ABS, author = "J.-D. Cao and H. H. Gonska", title = "Approximation by {Boolean} sums of positive linear operators. {II}. {Gopengauz}-type estimates", journal = j-J-APPROX-THEORY, volume = "57", number = "1", pages = "77--89", month = apr, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72266", catcode = "G.1.2; G.1.2; G.3; G.2.1", CRclass = "G.1.2 Approximation; G.1.2 Nonlinear approximation; G.1.2 Approximation; G.1.2 Elementary function approximation; G.3 Statistical computing; G.2.1 Combinatorics; G.2.1 Generating functions", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Generating functions", genterm = "algorithms; theory; measurement", guideno = "1989-07823", journalabbrev = "J. Approx. Theory", jrldate = "April 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS", } @Article{Chen:1989:EMB, author = "X. R. Chen and P. R. Krishnaiah and W. W. Liang", title = "Estimation of multivariate binary density using orthogonal functions", journal = j-J-MULTIVAR-ANAL, volume = "31", number = "2", pages = "178--186", month = nov, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh, Pittsburgh, PA", bibno = "69313", catcode = "D.3.3; G.3; G.1.3; G.1.2", CRclass = "D.3.3 Language Constructs; D.3.3 Procedures, functions, and subroutines; G.3 Statistical computing; G.1.3 Numerical Linear Algebra; G.1.3 Linear systems (direct and iterative methods); G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Software, PROGRAMMING LANGUAGES, Language Constructs, Procedures, functions, and subroutines; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods); Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; verification", guideno = "1989-08483", journalabbrev = "J. Multivariate Anal.", jrldate = "Nov. 1989", subject = "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Corliss:1989:IIV, author = "George Corliss and Gary Krenz", editor = "L. Gatteschi", title = "Indefinite Integration with Validation", journal = j-TOMS, volume = "15", number = "4", pages = "375--393", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65-04)", MRnumber = "1 062 497", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/76915.html; http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/", acknowledgement = ack-nhfb, bibno = "393", content = "ALGORITHMS; THEORY", CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Chebyshev approximation and theory", CRnumber = "1989-03199", descriptor = "mathematics of computing, numerical analysis, quadrature and numerical differentiation; mathematics of computing, numerical analysis, approximation, elementary function approximation; mathematics of computing, numerical analysis, approximation, Chebyshev approximation and theory", fortitle = "ACM Trans. Math. Softw.", guideno = "4", keywords = "algorithms; theory", review = "ACM CR 9007-0598", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory.", waffil = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Dehling:1989:FLI, author = "Herold Dehling", title = "The functional law of the iterated logarithm for {von Mises} functionals and multiple {Wiener} integrals", journal = j-J-MULTIVAR-ANAL, volume = "28", number = "2", pages = "177--189", month = feb, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG", bibno = "64336", catcode = "G.3; G.1.9; G.1.2", CRclass = "G.3 Statistical computing; G.1.9 Integral Equations; G.1.9 Integro-differential equations; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Integro-differential equations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; measurement", guideno = "1989-08462", journalabbrev = "J. Multivariate Anal.", jrldate = "February 1989", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Demirbas:1989:MSE, author = "K. Demirbas", title = "Multidimensional state estimation using stacks for dynamic systems with interference", journal = j-AUTOMATICA, volume = "25", number = "4", pages = "617--621", month = jul, year = "1989", CODEN = "ATCAA9", ISSN = "0005-1098", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72661", catcode = "G.1.2; G.1.2; G.1.3; G.1.5; H.1.1", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Linear approximation; G.1.3 Numerical Linear Algebra; G.1.3 Linear systems (direct and iterative methods); G.1.5 Roots of Nonlinear Equations; H.1.1 Systems and Information Theory; H.1.1 Information theory", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods); Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations; Information Systems, MODELS AND PRINCIPLES, Systems and Information Theory, Information theory", genterm = "algorithms; theory", guideno = "1989-03952", jrldate = "July 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H. Information Systems; H.1 MODELS AND PRINCIPLES", } @TechReport{Dritz:1989:RPS, author = "K. W. Dritz", title = "Rationale for the Proposed Standard for a Generic Package of Elementary Functions for {Ada}", type = "Report", number = "ANL-89/2 Rev. 1", institution = "Argonne National Laboratory, Mathematics and Computer Science Division", address = "Argonne, IL, USA", pages = "????", month = oct, year = "1989", bibdate = "Thu Sep 01 12:08:24 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @InProceedings{Duprat:1989:SRA, author = "J. Duprat and Y. Herreros and J.-M. Muller", title = "Some results about on-line computation of functions", crossref = "Ercegovac:1989:PSC", pages = "112--118", year = "1989", bibdate = "Sat Nov 27 14:19:10 MST 2004", acknowledgement = ack-nhfb, } @Article{Dyn:1989:PEB, author = "N. Dyn and A. Ron", title = "Periodic exponential box splines on a three direction mesh", journal = j-J-APPROX-THEORY, volume = "56", number = "3", pages = "287--296", month = mar, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72251", catcode = "G.1.2; F.2.2; G.1.2; G.1.2; G.1.2; G.2.1; G.3", CRclass = "G.1.2 Approximation; G.1.2 Spline and piecewise polynomial approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; G.1.2 Approximation; G.1.2 Chebyshev approximation and theory; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Linear approximation; G.2.1 Combinatorics; G.2.1 Recurrences and difference equations; G.3 Statistical computing", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Recurrences and difference equations; Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing", genterm = "algorithms; theory; design", guideno = "1989-07809", journalabbrev = "J. Approx. Theory", jrldate = "Mar. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS", } @Article{Eberlein:1989:SAC, author = "E. Eberlein", title = "Strong approximation of continuous time stochastic processes", journal = j-J-MULTIVAR-ANAL, volume = "31", number = "2", pages = "220--235", month = nov, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. Freiburg, Freiburg, W. Germany", bibno = "69316", catcode = "D.4.8; F.1.2; G.1.2", CRclass = "D.4.8 Performance; D.4.8 Stochastic analysis; F.1.2 Modes of Computation; F.1.2 Probabilistic computation; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Software, OPERATING SYSTEMS, Performance, Stochastic analysis; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Probabilistic computation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; performance; theory", guideno = "1989-08486", journalabbrev = "J. Multivariate Anal.", jrldate = "Nov. 1989", subject = "D. Software; D.4 OPERATING SYSTEMS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Egger:1989:PAC, author = "A. Egger and R. Huotari", title = "The {Polya} algorithm on convex sets", journal = j-J-APPROX-THEORY, volume = "56", number = "2", pages = "212--216", month = feb, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72242", catcode = "F.2.2; F.2.2; G.1.2; G.1.2; G.1.5", CRclass = "F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Computations on discrete structures; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms; G.1.5 Roots of Nonlinear Equations; G.1.5 Convergence", descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence", genterm = "algorithms; theory", guideno = "1989-07801", journalabbrev = "J. Approx. Theory", jrldate = "Feb. 1989", subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Ehrenmark:1989:ONF, author = "Ulf T. Ehrenmark", title = "Overconvergence of the near-field expansion for linearized waves normally incident on a sloping beach", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "799--815", month = jun, year = "1989", CODEN = "SMJMAP", ISSN = "0036-1399", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64945", catcode = "G.1.7; G.1.2; F.2.1; G.1.2; F.2.2", CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations", genterm = "algorithms; theory; experimentation", guideno = "1989-09714", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @Article{Einmahl:1989:ERK, author = "U. Einmahl", title = "Extensions of results of {Komlos}, {Major}, and {Tusnady} to the multivariate case", journal = j-J-MULTIVAR-ANAL, volume = "28", number = "1", pages = "20--68", month = jan, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. zu Koln, West Germany", bibno = "66700", catcode = "G.3; G.1.2; F.2.1", CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms", genterm = "algorithms; theory", guideno = "1989-08456", journalabbrev = "J. Multivariate Anal.", jrldate = "Jan. 1989", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", } @Article{Epperson:1989:UIM, author = "J. F. Epperson", title = "On the use of iteration methods for approximating the natural logarithm", journal = j-AMER-MATH-MONTHLY, volume = "96", number = "9", pages = "831--835", month = nov, year = "1989", CODEN = "AMMYAE", ISSN = "0002-9890", MRclass = "26A06 (26A09)", MRnumber = "91a:26002", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "71703", catcode = "G.1.2; G.1.2; K.3.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Spline and piecewise polynomial approximation; K.3.2 Computer and Information Science Education", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation; Computing Milieux, COMPUTERS AND EDUCATION, Computer and Information Science Education", genterm = "algorithms; theory", guideno = "1989-03518", journalabbrev = "Am. Math. Monthly", jrldate = "Nov. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K. Computing Milieux; K.3 COMPUTERS AND EDUCATION", } @Article{Ge:1989:OCL, author = "Renpu Ge", title = "Optimal choice of linear interval extension", journal = j-APPL-MATH-COMP, volume = "30", number = "2", pages = "165--189", month = mar, year = "1989", CODEN = "AMHCBQ", ISSN = "0096-3003", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64710", catcode = "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1; G.1.0", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2 Approximation; G.1.2 Linear approximation; G.1.2 Approximation; G.1.2 Elementary function approximation; G.2.1 Combinatorics; G.2.1 Combinatorial algorithms; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Computations on discrete structures; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms; G.1.1 Interpolation; G.1.1 Difference formulas; G.1.0 General; G.1.0 Numerical algorithms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Difference formulas; Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms", genterm = "algorithms; theory; measurement", guideno = "1989-03670", journalabbrev = "Appl. Math. Comput.", jrldate = "March 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Gersch:1989:SPT, author = "W. Gersch and G. Kitagawa", title = "Smoothness priors transfer function estimation", journal = j-AUTOMATICA, volume = "25", number = "4", pages = "603--608", month = jul, year = "1989", CODEN = "ATCAA9", ISSN = "0005-1098", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72658", catcode = "G.1.1; G.1.2; G.1.6", CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.6 Optimization; G.1.6 Gradient methods", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods", genterm = "algorithms; theory", guideno = "1989-03949", jrldate = "July 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InCollection{Glover:1989:THN, author = "Keith Glover", editor = "Jan C. Willems", booktitle = "From data to model", title = "A tutorial on {Hankel}-norm approximation", publisher = pub-SV, address = pub-SV:adr, pages = "26--48", year = "1989", ISBN = "0-387-51571-2", ISBN-13 = "978-0-387-51571-7", LCCN = "QA279 .F76 1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "70545", bookpages = "246", catcode = "G.1.2; F.2.1; F.2.1", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms", genterm = "algorithms; theory", guideno = "1989-01692", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY", waffil = "Univ. of Groningen, Groningen, The Netherlands", } @InProceedings{Glynn:1989:OSS, author = "P. W. Glynn", editor = "Edward A. MacNair and Kenneth J. Musselman and Philip Heidelberger", booktitle = "1989 Winter Simulation Conference proceedings: December 4--6, 1989, the Capital Hilton Hotel, Washington, DC", title = "Optimization of stochastic systems via simulation", publisher = pub-ACM, address = pub-ACM:adr, pages = "90--105", year = "1989", ISBN = "0-911801-58-8", ISBN-13 = "978-0-911801-58-3", LCCN = "QA76.9.C65 W56 1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", note = "IEEE order no. 89CH2778-9.", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5823", acknowledgement = ack-nhfb, bibno = "76750", bookpages = "xx + 1139", catcode = "I.6.3; G.1.6; G.3; G.1.2", CRclass = "I.6.3 Applications; G.1.6 Optimization; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Computing Methodologies, SIMULATION AND MODELING, Applications; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization; Mathematics of Computing, PROBABILITY AND STATISTICS; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; design; performance", guideno = "1989-12012", procdate = "December 4-6, 1989", procloc = "Washington, D. C.", subject = "I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Gomes:1989:GGL, author = "M. I. Gomes", title = "Generalized {Gumbel} and likelihood ratio test statistics in the multivariate {GEV} model", journal = j-COMPUT-STAT-DATA-ANAL, volume = "7", number = "3", pages = "259--267", month = feb, year = "1989", CODEN = "CSDADW", ISSN = "0167-9473", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "70043", catcode = "G.3; G.1.7; I.5.1; G.1.6; G.1.2", CRclass = "G.3 Statistical computing; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; I.5.1 Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Computing Methodologies, PATTERN RECOGNITION, Models, Statistical; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; measurement; reliability; theory", guideno = "1989-04403", journalabbrev = "Comput. Stat. Data Anal.", jrldate = "Feb. 1989", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.5 PATTERN RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Gonzaga:1989:ASL, author = "Cl{\'o}vis C. Gonzaga", title = "An algorithm for solving linear programming programs in {$O(n^3L)$} operations", crossref = "Megiddo:1989:PMP", pages = "1--28", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "74172", catcode = "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; I.1.2 Algorithms; I.1.2 Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis of algorithms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms", genterm = "algorithms; theory", guideno = "1989-12474", procdate = "March 1-4, 1987", procloc = "Pacific Grove, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION", } @Article{Guo:1989:RCS, author = "S.-S. Guo and M. K. Khan", title = "On the rate of convergence of some operators on functions of bounded variation", journal = j-J-APPROX-THEORY, volume = "58", number = "1", pages = "90--101", month = jul, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "69424", catcode = "F.2.1; G.1.2", CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on polynomials; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "1989-07854", journalabbrev = "J. Approx. Theory", jrldate = "July 1989", subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Hornik:1989:MFN, author = "K. Hornik and M. Stinchcombe and H. White", title = "Multilayer feedforward networks are universal approximators", journal = j-NEURAL-NETWORKS, volume = "2", number = "5", pages = "359--366", year = "1989", CODEN = "NNETEB", ISSN = "0893-6080", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Technisce Univ. Wien, Vienna, Austria; Univ. of California, San Diego; Univ. of California, San Diego", bibno = "70408", catcode = "F.2.1; G.1.2; F.1.1; I.2.4", CRclass = "F.2.1 Numerical Algorithms and Problems; G.1.2 Approximation; G.1.2 Elementary function approximation; F.1.1 Models of Computation; F.1.1 Unbounded-action devices; I.2.4 Knowledge Representation Formalisms and Methods", descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Unbounded-action devices; Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods", genterm = "design; performance", guideno = "1989-09273", journalabbrev = "Neural Networks", jrldate = "1989", subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE", } @Article{Jeffries:1989:GFA, author = "John S. Jeffries and Donald R. Smith", title = "A {Green} function approach for a singularly perturbed vector boundary-value problem", journal = j-ADV-APPL-MATH, volume = "10", number = "1", pages = "1--50", month = mar, year = "1989", CODEN = "????", ISSN = "0196-8858", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of California at San Diego, La Jolla; Univ. of California at San Diego, La Jolla", bibno = "64833", catcode = "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3", CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Boundary value problems; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability; F.2.1 Numerical Algorithms and Problems; F.2.1 Computation of transforms; G.1.2 Approximation; G.1.2 Nonlinear approximation; G.1.3 Numerical Linear Algebra; G.1.3 Eigenvalues; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.3 Numerical Linear Algebra; G.1.3 Linear systems (direct and iterative methods)", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods)", genterm = "algorithms; theory", guideno = "1989-03271", journalabbrev = "Adv. Appl. Math.", jrldate = "March 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Kaishev:1989:SSC, author = "A. I. Kaishev", title = "A sharpened scheme for constructing an a posteriori interval extension of an elementary function. ({Russian})", journal = "Voprosy Kibernet. (Moscow)", volume = "149", pages = "14--18", year = "1989", ISBN = "0134-6388", ISBN-13 = "0134-6388", MRclass = "65G10", MRnumber = "91i:65090", MRreviewer = "I. N. Molchanov", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Kogan:1989:GBF, author = "B. J. Kogan", title = "General background of functional memory algorithms", journal = j-TRANS-SOC-COMP-SIM, volume = "5", number = "4", pages = "285--317", month = oct, year = "1989", CODEN = "TSCSEV", ISSN = "0740-6797", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of California, Los Angeles", bibno = "69149", catcode = "C.3; G.1.2; G.1.2; E.4", CRclass = "C.3 Signal processing systems; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Linear approximation; E.4 Data compaction and compression", descriptor = "Computer Systems Organization, SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal processing systems; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Data, CODING AND INFORMATION THEORY, Data compaction and compression", genterm = "algorithms; design", guideno = "1989-10680", journalabbrev = "Trans. Soc. Comput. Simul.", jrldate = "Oct. 1989", subject = "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING AND INFORMATION THEORY", } @InProceedings{Kojima:1989:PDI, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "A primal-dual interior point algorithm for linear programming", crossref = "Megiddo:1989:PMP", pages = "29--47", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "74173", bookpages = "x + 158", catcode = "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.1 Numerical Algorithms and Problems; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; I.1.2 Algorithms; I.1.2 Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis of algorithms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms", genterm = "algorithms; theory", guideno = "1989-12475", procdate = "March 1-4, 1987", procloc = "Pacific Grove, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION", } @Article{Kraaikamp:1989:SEP, author = "Cor Kraaikamp", title = "Statistic and ergodic properties of {Minkowski}'s diagonal continued fraction", journal = j-THEOR-COMP-SCI, volume = "65", number = "2", pages = "197--212", day = "28", month = jun, year = "1989", CODEN = "TCSCDI", ISSN = "0304-3975", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Amsterdam Univ., Amsterdam, The Netherlands and Univ. de Provence, Marseille, France", bibno = "70095", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "1989-10594", journalabbrev = "Theor. Comput. Sci.", jrldate = "28 June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Kreider:1989:WSA, author = "K. L. Kreider", title = "A wave splitting approach to time dependent inverse scattering for the stratified cylinder", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "932--943", month = jun, year = "1989", CODEN = "SMJMAP", ISSN = "0036-1399", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64953", catcode = "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1", CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Initial value problems; G.1.2 Approximation; G.1.2 Elementary function approximation; J.2 Physics; J.2 Electronics; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; G.1.3 Numerical Linear Algebra; G.1.3 Linear systems (direct and iterative methods); I.1.1 Expressions and Their Representation; I.1.1 Simplification of expressions", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Electronics; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods); Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions", genterm = "algorithms; theory; experimentation; measurement", guideno = "1989-09722", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION", } @PhdThesis{Littlestone:1989:MBL, author = "N. Littlestone", title = "Mistake bounds and logarithmic linear-threshold learning algorithms", type = "{Ph.D} Thesis", school = "University of California at Santa Cruz", address = "Santa Cruz, CA, USA", pages = "????", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "76493", catcode = "I.2.6; J.4; H.1.2; G.1.2", CRclass = "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine Systems; H.1.2 Human information processing; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE, Learning; Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Psychology; Information Systems, MODELS AND PRINCIPLES, User/Machine Systems, Human information processing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; human factors; performance", guideno = "1989-12934", source = "UMI Order No: GAX89-26506", subject = "I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Lo:1989:RBP, author = "Shaw-Hwa Lo and Jane-Ling Wang", title = "Representations for the bivariate product limit estimators and the bootstrap versions", journal = j-J-MULTIVAR-ANAL, volume = "28", number = "2", pages = "211--226", month = feb, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of California, Davis; Univ. of California, Davis", bibno = "64339", catcode = "G.3; G.1.2; G.1.4; G.1.7", CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.4 Quadrature and Numerical Differentiation; G.1.4 Gaussian quadrature; G.1.7 Ordinary Differential Equations; G.1.7 Convergence and stability", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature; Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Convergence and stability", genterm = "algorithms; theory; measurement", guideno = "1989-08465", journalabbrev = "J. Multivariate Anal.", jrldate = "February 1989", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Lorentz:1989:NA, author = "G. G. Lorentz", title = "Notes on approximation", journal = j-J-APPROX-THEORY, volume = "56", number = "3", pages = "360--365", month = mar, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72258", catcode = "G.1.1; G.1.2; G.1.1", CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.1 Interpolation; G.1.1 Spline and piecewise polynomial interpolation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation", genterm = "algorithms; theory", guideno = "1989-07816", journalabbrev = "J. Approx. Theory", jrldate = "Mar. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Megiddo:1989:POS, author = "N. Megiddo", title = "Pathways to the optimal set in linear programming", crossref = "Megiddo:1989:PMP", pages = "131--158", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "74179", catcode = "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4; G.4", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2 Approximation; G.1.2 Elementary function approximation; G.2.2 Graph Theory; G.2.2 Path and circuit problems; G.1.2 Approximation; G.1.2 Spline and piecewise polynomial approximation; G.1.5 Roots of Nonlinear Equations; G.1.5 Iterative methods; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; I.1.2 Algorithms; I.1.2 Analysis of algorithms; G.4 Algorithm analysis; G.4 Efficiency", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Path and circuit problems; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms; Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency", genterm = "algorithms; performance; theory", guideno = "1989-12481", procdate = "March 1-4, 1987", procloc = "Pacific Grove, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE", } @PhdThesis{Miler:1989:EEM, author = "T. H. Miler", title = "Error evaluation of microcomputer intrinsic functions", type = "{Ph.D} Thesis", school = "University of Idaho", address = "Moscow, ID", pages = "????", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "76168", catcode = "G.4; G.1.2; J.2", CRclass = "G.4 Reliability and robustness; G.1.2 Approximation; G.1.2 Elementary function approximation; J.2 Mathematics and statistics", descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics", genterm = "algorithms; reliability", guideno = "1989-12941", source = "UMI order no: GAX89-22813", subject = "G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING", } @InProceedings{Montuschi:1989:EIH, author = "P. Montuschi and L. Ciminiera", title = "On the efficient implementation of higher radix square root algorithms", crossref = "Ercegovac:1989:PSC", pages = "154--161", year = "1989", bibdate = "Sat Nov 27 14:19:10 MST 2004", acknowledgement = ack-nhfb, } @Book{Moshier:1989:MPM, author = "Stephen L. B. Moshier", title = "Methods and Programs for Mathematical Functions", publisher = pub-ELLIS-HORWOOD, address = pub-ELLIS-HORWOOD:adr, pages = "vii + 415", year = "1989", ISBN = "0-7458-0289-3", ISBN-13 = "978-0-7458-0289-3", LCCN = "QA331 .M84 1989", bibdate = "Thu Sep 01 10:33:40 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", price = "US\pounds 48.00", acknowledgement = ack-nj, } @Article{Rhee:1989:MII, author = "W. T. Rhee and M. Talagrand", title = "Martingale inequalities, interpolation and {NP}-complete problems", journal = j-MATH-OP-RES, volume = "14", number = "1", pages = "91--96", month = feb, year = "1989", CODEN = "MOREDQ", ISSN = "0364-765X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ., Paris, Paris, France; Ohio State Univ., Columbus", bibno = "67063", catcode = "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3", CRclass = "G.2.2 Graph Theory; G.2.2 Path and circuit problems; H.1.1 Systems and Information Theory; H.1.1 General systems theory; G.1.1 Interpolation; G.1.1 Interpolation formulas; G.1.2 Approximation; G.1.2 Elementary function approximation; G.3 Probabilistic algorithms (including Monte Carlo); I.6.4 Model Validation and Analysis; F.1.3 Complexity Classes; F.1.3 Reducibility and completeness", descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Path and circuit problems; Information Systems, MODELS AND PRINCIPLES, Systems and Information Theory, General systems theory; Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo); Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes, Reducibility and completeness", genterm = "algorithms; theory; measurement", guideno = "1989-09079", journalabbrev = "Math. Oper. Res.", jrldate = "Feb. 1989", subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; H. Information Systems; H.1 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; I. Computing Methodologies; I.6 SIMULATION AND MODELING; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES", } @Article{Ruymgaart:1989:SPB, author = "F. H. Ruymgaart", title = "Some properties of bivariate empirical hazard processes under random censoring", journal = j-J-MULTIVAR-ANAL, volume = "28", number = "2", pages = "271--281", month = feb, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64343", catcode = "G.3; G.1.2", CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory; measurement", guideno = "1989-08469", journalabbrev = "J. Multivariate Anal.", jrldate = "February 1989", subject = "G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InCollection{Saigo:1989:FID, author = "Megumi Saigo", title = "Fractional integrals and derivatives associated with elementary functions and {Bessel} functions", crossref = "Srivastava:1989:UFF", pages = "283--306", year = "1989", MRclass = "26A33 (33C10)", MRnumber = "93h:26011", bibdate = "Sat Jan 11 17:44:01 MST 1997", series = "Ellis Horwood Ser. Math. Appl.", acknowledgement = ack-nhfb, } @Article{Smith:1989:EMP, author = "David M. Smith", title = "Efficient multiple-precision evaluation of elementary functions", journal = j-MATH-COMP, volume = "52", number = "185", pages = "131--134", month = jan, year = "1989", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D15 (26-04)", MRnumber = "90c:65034", MRreviewer = "Menachem Dishon", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4120 (Functional analysis)", corpsource = "Dept. of Math., Loyola Univ., Los Angeles, CA, USA", keywords = "arithmetic; base b; elementary functions; function evaluation; multiple-precision evaluation", treatment = "T Theoretical or Mathematical", } @TechReport{Tang:1989:TCA, author = "Ping Tak Peter Tang", title = "Testing Computer Arithmetic by Elementary Number Theory", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", address = "Argonne, IL, USA", pages = "????", month = aug, year = "1989", bibdate = "Fri Jun 11 12:38:06 1999", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Tang:1989:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Exponential Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "15", number = "2", pages = "144--157", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:47:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/; http://doi.acm.org/10.1145/63522.214389", abstract = "Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.", acknowledgement = ack-nj, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Ubhaya:1989:LAN, author = "V. A. Ubhaya", title = "{$L_p$} approximation from nonconvex subsets of special classes of functions", journal = j-J-APPROX-THEORY, volume = "57", number = "2", pages = "223--238", month = may, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72277", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1989-07833", journalabbrev = "J. Approx. Theory", jrldate = "May 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @InProceedings{Vaidya:1989:LWB, author = "P. M. Vaidya", title = "A locally well-behaved potential function and a simple {Newton}-type method for finding the center of a polytype", crossref = "Megiddo:1989:PMP", pages = "79--90", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "74176", catcode = "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.6 Optimization; G.1.6 Gradient methods; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.5 Roots of Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of Nonlinear Equations; G.1.5 Iterative methods; I.1.2 Algorithms; I.1.2 Nonalgebraic algorithms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms", genterm = "algorithms; theory", guideno = "1989-12478", procdate = "March 1-4, 1987", procloc = "Pacific Grove, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION", xxpages = "131--158", } @PhdThesis{Vavasis:1989:CFP, author = "S. A. Vavasis", title = "Complexity of fixed point computations", type = "{Ph.D} Thesis", school = "Stanford University", address = "Stanford, CA, USA", pages = "????", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "76220", catcode = "J.4; G.1.2; F.1.3; G.1.2; G.2.2", CRclass = "J.4 Economics; G.1.2 Approximation; G.1.2 Nonlinear approximation; F.1.3 Complexity Classes; G.1.2 Approximation; G.1.2 Elementary function approximation; G.2.2 Graph Theory; G.2.2 Network problems", descriptor = "Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Economics; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems", genterm = "algorithms; theory", guideno = "1989-12859", source = "UMI order no: GAX89-19486", subject = "J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS", } @InProceedings{Vial:1989:APP, author = "J.-P. Vial", title = "Approximate projections in a projective method for the linear feasibility problem", crossref = "Megiddo:1989:PMP", pages = "65--78", year = "1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "74175", bookpages = "x + 158", catcode = "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.2 Nonnumerical Algorithms and Problems; F.2.2 Geometrical problems and computations; I.1.2 Algorithms; I.1.2 Nonalgebraic algorithms; G.1.6 Optimization; G.1.6 Constrained optimization; G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.2.1 Computations on matrices; G.1.2 Approximation; G.1.2 Minimax approximation and algorithms", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations; Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms", genterm = "algorithms; experimentation; measurement; performance; theory", guideno = "1989-12477", procdate = "March 1-4, 1987", procloc = "Pacific Grove, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{vonRosen:1989:MLE, author = "D. von Rosen", title = "Maximum likelihood estimators in multivariate linear normal models", journal = j-J-MULTIVAR-ANAL, volume = "31", number = "2", pages = "187--200", month = nov, year = "1989", CODEN = "JMVAAI", ISSN = "0047-259X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Stockholm, Stockholm, Sweden", bibno = "69314", catcode = "G.1.6; G.1.2; G.1.2", CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2 Approximation; G.1.2 Linear approximation; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Linear approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "1989-08484", journalabbrev = "J. Multivariate Anal.", jrldate = "Nov. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Wasilkowski:1989:AIV, author = "G. W. Wasilkowski", title = "On adaptive information with varying cardinality for linear problems with elliptically contoured measures", journal = j-J-COMPLEXITY, volume = "5", number = "3", pages = "363--368", month = sep, year = "1989", CODEN = "JOCOEH", ISSN = "0885-064X", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, affiliation = "Univ. of Kentucky, Lexington, KY", bibno = "68756", catcode = "G.1.2; G.1.2; F.1.3", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.2 Approximation; G.1.2 Nonlinear approximation; F.1.3 Complexity Classes", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes", genterm = "algorithms; theory", guideno = "1989-08045", journalabbrev = "J. Complexity", jrldate = "Sept. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES", } @Article{Yortsos:1989:LSI, author = "Y. C. Yortsos and F. J. Hickernell", title = "Linear stability of immiscible displacement in porous media", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "730--748", month = jun, year = "1989", CODEN = "SMJMAP", ISSN = "0036-1399", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "64942", catcode = "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8", CRclass = "G.1.8 Partial Differential Equations; G.1.8 Parabolic equations; G.1.0 General; G.1.0 Stability (and instability); J.2 Earth and atmospheric sciences; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.4 Quadrature and Numerical Differentiation; G.1.4 Finite difference methods; G.1.8 Partial Differential Equations; G.1.8 Difference methods", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Parabolic equations; Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability); Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Earth and atmospheric sciences; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Finite difference methods; Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods", genterm = "algorithms; theory; experimentation", guideno = "1989-09711", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Zalik:1989:NIE, author = "R. A. Zalik", title = "A new inequality for entire functions", journal = j-J-APPROX-THEORY, volume = "58", number = "3", pages = "281--283", month = sep, year = "1989", CODEN = "JAXTAZ", ISSN = "0021-9045", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", acknowledgement = ack-nhfb, bibno = "72294", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "verification; theory", guideno = "1989-07871", journalabbrev = "J. Approx. Theory", jrldate = "Sept. 1989", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Book{Ziemer:1989:WDF, author = "William P. Ziemer", title = "Weakly differentiable functions: {Sobolev} spaces and functions of bounded variation", volume = "120", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 308", year = "1989", ISBN = "0-387-97017-7", ISBN-13 = "978-0-387-97017-2", LCCN = "QA323 .Z53 1989", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", series = "Graduate texts in mathematics", acknowledgement = ack-nhfb, affiliation = "Indiana Univ., Bloomington", bibno = "69369", catcode = "G.1.2; G.1.8; G.1.5", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.8 Partial Differential Equations; G.1.5 Roots of Nonlinear Equations", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations; Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations", genterm = "algorithms; theory", guideno = "1989-01732", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Article{Bronstein:1990:IEF, author = "Manuel Bronstein", title = "Integration of elementary functions", journal = j-J-SYMBOLIC-COMP, volume = "9", number = "2", pages = "117--173", month = feb, year = "1990", CODEN = "JSYCEH", ISSN = "0747-7171", MRclass = "12H05 (68Q40)", MRnumber = "91h:12017", MRreviewer = "Alexandru Buium", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "Theory/cathode.bib", acknowledgement = ack-nhfb, classcodes = "C1120 (Analysis); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", keywords = "algebraic extension; algebraic function; decision procedure; elementary function field; elementary functions; exponential; finite terms; indefinite; integration; integration Risch ODEs oderef; logarithm; proof; Trager", treatment = "T Theoretical or Mathematical", } @Article{Carre:1990:PEF, author = "C. Carre", title = "Plethysm of elementary functions", journal = "Bayreuth. Math. Schr.", volume = "31", pages = "1--18", year = "1990", ISSN = "0172-1062", MRclass = "20C30 (05E05 22E45)", MRnumber = "91f:20013", MRreviewer = "John R. Stembridge", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Cody:1990:PEP, author = "W. J. Cody", title = "Performance Evaluation of Programs for the Error and Complementary Error Functions", journal = j-TOMS, volume = "16", number = "1", pages = "29--37", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "http://dx.doi.org/10.1145/77626.77628", ISSN = "0098-3500", MRclass = "65-04 (65G05)", MRnumber = "1 073 407", bibdate = "Tue Oct 09 09:29:47 2007", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib, ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html", abstract = "This paper presents methods for performance evaluation of computer programs for the functions $\textrm{erf}(x)$, $\textrm{erfc}(x)$, and $\e^{x^2} \textrm{erfc}(x)$. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of $\textrm{erfc}(x)$. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.", acknowledgement = ack-nhfb, affiliation = "Argonne Nat. Lab., IL, USA", classification = "B0290F (Interpolation and function approximation); B0290B (Error analysis in numerical methods); C4130 (Interpolation and function approximation); C4110 (Error analysis in numerical methods)", keywords = "FORTRAN; Complementary error functions; Computer programs; Power series expansions; Repeated integrals; Robustness; Test program", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", thesaurus = "Error analysis; Function approximation; Performance evaluation", } @Article{Dunham:1990:FPF, author = "C. B. Dunham", title = "Feasibility of ``perfect'' function evaluation", journal = j-SIGNUM, volume = "25", number = "4", pages = "25--26", month = oct, year = "1990", CODEN = "SNEWD6", DOI = "http://doi.acm.org/10.1145/122272.122276", ISSN = "0163-5778", bibdate = "Tue Apr 12 07:50:19 MDT 2005", bibsource = "http://portal.acm.org/; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb # " and " # ack-nj, } @InProceedings{Kiernan:1990:FAE, author = "J. M. Kiernan and T. B. Blachowiak", title = "Fast, Accurate Elementary Functions For the {Cray Y-MP} Computer", crossref = "Cray:1990:PCU", pages = "243--252", year = "1990", bibdate = "Thu Sep 1 10:15:30 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Koren:1990:EEF, author = "I. Koren and O. Zinaty", title = "Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations", journal = j-IEEE-TRANS-COMPUT, volume = "C-39", number = "8", pages = "1030--1037", month = aug, year = "1990", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Sep 1 10:15:30 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Markstein:1990:CEF, author = "P. W. Markstein", title = "Computation of elementary functions on the {IBM RISC System\slash 6000} processor", journal = j-IBM-JRD, volume = "34", number = "1", pages = "111--119", month = jan, year = "1990", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65-04 (65D20)", MRnumber = "1 057 659", bibdate = "Sat Jan 11 17:44:01 MST 1997", abstract = "The additional speed and precision of the IBM RISC System\slash 6000 floating-point unit have motivated reexamination of algorithms to perform division, square root, and the elementary functions. New results are obtained which avoid the necessity of doing special testing to get the last bit rounded correctly in accordance with all of the IEEE rounding modes in the case of division and square root. For the elementary function library, a technique is described for always getting the last bit rounded correctly in the selected IEEE rounding mode.", acknowledgement = ack-nhfb, affiliation = "IBM Res. Div., Austin, TX, USA", classification = "C5230 (Digital arithmetic methods)", keywords = "Division; Elementary functions; Floating-point unit; IBM RISC System\slash 6000 processor; IEEE rounding modes; IEEE rounding modes, IBM RISC System/6000 processor; Square root", thesaurus = "Digital arithmetic; IBM computers; Reduced instruction set computing", } @InCollection{Mora:1990:EFI, author = "Gerardo Mora and Edwin Castro and Ioan Muntean", booktitle = "Mathematics in Costa Rica, Vol. 1 (Spanish) (San Jos{\'e}, 1990),", title = "Elementary functions. {I}. ({Spanish})", publisher = "Univ. Costa Rica", address = "San Jos{\'e}, Costa Rica", pages = "76--86", year = "1990", MRclass = "26A09", MRnumber = "1 111 714", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @MastersThesis{Muller:1990:HCA, author = "Volker M{\"u}ller", title = "{Hochgenaue {CORDIC}-Algorithmen f{\"u}r reelle Standardfunktionen mittels dynamischer Defektberechnung} \toenglish {High-accuracy {CORDIC} Algorithms for Real Elementary Functions by Means of Dynamic Error Computation} \endtoenglish", type = "Diplomarbeit", school = "Institut f{\"u}r angewandte Mathematik, Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", month = dec, year = "1990", bibdate = "Fri Jun 11 12:38:17 1999", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Palmore:1990:CAC, author = "J. Palmore and C. Herring", title = "Computer arithmetic, chaos and fractals", journal = j-PHYSICA-D, volume = "42", number = "1-3", pages = "99--110", month = jun, year = "1990", CODEN = "PDNPDT", ISSN = "0167-2789", bibdate = "Tue Dec 12 09:17:24 MST 1995", note = "Ninth Annual International Conference of the Center for Nonlinear Studies on Self-Organizing, Collective and Cooperative Phenomena in Natural and Artificial Networks", abstract = "The authors explore aspects of computer arithmetic from the viewpoint of dynamical systems. They demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. They show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Illinois Univ., Urbana, IL, USA", classification = "C5230 (Digital arithmetic methods); C1160 (Combinatorial mathematics)", confdate = "22-26 May 1989", conflocation = "Los Alamos, NM, USA", keywords = "Self-similar structure; Chaos; Computer arithmetic; Dynamical systems; Finite precision arithmetic; Uniformly hyperbolic chaotic dynamical systems; Bernoulli shifts; Cat maps; Pseudorandom number generators; Elementary floating-point operations; Binary computer arithmetic; Fractal structure; Dynamical systems; Integer arithmetic; Floating-point arithmetic", language = "English", pubcountry = "Netherlands", thesaurus = "Chaos; Digital arithmetic; Fractals; Random number generation; Roundoff errors", } @Book{Swartzlander:1990:CA, author = "Earl E. Swartzlander", title = "Computer arithmetic", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "various", year = "1990", ISBN = "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1 microfiche)", ISBN-13 = "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1 microfiche)", LCCN = "QA76.6.C633 1990", bibdate = "Sat Feb 24 15:01:45 MST 1996", note = "Two volumes.", series = "IEEE Computer Society Press tutorial", acknowledgement = ack-nhfb, annote = "Vol. 1 is a reprint. Originally published: Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980. Originally published in series: Benchmark papers in electrical engineering and computer science; 21. Vol 2 is a sequel to the earlier collection. Vol. 1: 2nd ed. Includes bibliographical references and index. Arithmetic operations in a binary computer / R.F. Shaw --- High-speed arithmetic in binary computers / O.L. MacSorley --- Fast carry logic for digital computers / B. Gilchrist, J.H. Pomerene, and S.Y. Wong --- A logic for high-speed addition / A. Weinberger and J.L. Smith --- Conditional-sum addition logic / J. Sklansky --- An evaluation of several two-summand binary adders / J. Sklansky - - Adder with distributed control / A. Svoboda --- Multiple addition by residue threshold functions and their representation by array logic / I.T. Ho and T.C. Chen --- Counting responders in an associative memory / C.C. Foster and F.D. Stockton --- Parallel counters / E.E. Swartzlander, Jr. --- A signed binary multiplication technique / A.D. Booth --- Multiplying made easy for digital assemblies / C. Ghest. A binary multiplication scheme based on squaring / T.C. Chen --- A suggestion for a fast multiplier / C.S. Wallace --- Some schemes for parallel multipliers / L. Dadda --- On parallel digital multipliers / L. Dadda --- A compact high-speed parallel multiplication scheme / W.J. Stenzel, W.J. Kubitz, and G.H. Garcia --- A two's complement parallel array multiplication algorithm / C.R. Baugh and B.A. Wooley --- Comments on ``A two's complement parallel array multiplication algorithm'' / P.E. Blankenship --- The quasi-serial multiplier / E.E. Swartzlander, Jr. --- The two's complement quasi-serial multiplier / T.G. McDaneld and R.K. Guha --- A new class of digital division methods / J.E Robertson --- An algorithm for rapid binary division / J.B. Wilson and R.S. Ledley. Digit-by-digit transcendental-function computation / R.J. Linhardt and H.S.Miller --- A unified algorithm for elementary functions / J.S. Walther --- Some properties of iterative square-rooting methods using high-speed multiplication /C.V. Ramamoorthy, J.R. Goodman, and K.H. Kim --- Radix-16 evaluation of certain elementary functions / M.D. Ercegovac --- On the distribution of numbers / R.W. Hamming --- An analysis of floating-point addition / D.W. Sweeney --- The IBM\ldots{}Model 91: floating-point execution unit / S.F. Anderson \ldots{} [et al.] --Design of large high-speed floating-point-arithmetic units / J.B. Gosling --- Analysis of rounding methods in floating-point arithmetic / D.J. Kuck,D.S. Parker, Jr., and A.H. Sameh.cos x, tan-p1s x, and cot-p1s x / W.H. Specker.", keywords = "Electronic digital computers --- Programming.; Floating-point arithmetic.; Computer arithmetic.", } @Article{Tang:1990:AET, author = "Ping Tak Peter Tang", title = "Accurate and Efficient Testing of the Exponential and Logarithm Functions", journal = j-TOMS, volume = "16", number = "3", pages = "185--200", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65G99)", MRnumber = "1 070 797", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/; http://doi.acm.org/10.1145/79505.79506", abstract = "Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.", acknowledgement = ack-nhfb, keywords = "algorithms; languages; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @TechReport{Tang:1990:PGE, author = "Ping Tak Peter Tang", title = "A Portable Generic Elementary Function Package in {Ada} and an Accurate Test Suite", type = "Technical report", number = "ANL-90/35", institution = inst-ANL, address = inst-ANL:adr, pages = "iii + 35", month = nov, year = "1990", bibdate = "Fri Dec 28 11:36:25 2007", URL = "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF", abstract = "A comprehensive set of elementary functions has been implemented portably in Ada. The high accuracy of the implementation has been confirmed by rigorous analysis. Moreover, we present new test methods that are efficient and offer a high resolution of 0.005 unit in the last place, Tbese test methods have been implemented portably here and confirm the accuracy of our implemented functions. Reports on the accuracy of other function libraries obtained by our test programs are also presented.", acknowledgement = ack-nhfb, } @TechReport{Tang:1990:SSI, author = "Ping Tak Peter Tang", title = "Some Software Implementations of the Functions Sine and Cosine", type = "Technical report", number = "ANL-90/3", institution = inst-ANL, address = inst-ANL:adr, month = apr, year = "1990", bibdate = "Fri Dec 28 11:21:38 2007", URL = "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm", abstract = "This document presents several software implementations of the elementary functions sin and cos designed to fit a large class of machines. Implementation details are provided. Also provided is a detailed error analysis that bounds the errors of these implementations, over the full range of input arguments, from 0.721 to 0.912 units in the last place. Tests performed on these codes give results that are consistent with the error bounds.", acknowledgement = ack-nhfb, xxnote = "Where is this? I can find no electronic version online, other than the abstract at the given URL.", } @Article{Tang:1990:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Logarithm Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "16", number = "4", pages = "378--400", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:26:09 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/; http://doi.acm.org/10.1145/98267.98294", abstract = "Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.", acknowledgement = ack-nj, keywords = "algorithms; design; performance; reliability; standardization; theory; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Bartoloni:1991:MFU, author = "A. Bartoloni and C. Battista and S. Cabasino and N. Cabibbo and F. Del Prete and F. Marzano and P. S. Paolucci and R. Sarno and G. Salina and G. M. Todesco and M. Torelli and R. Tripiccione and W. Tross and E. Zanetti", title = "{MAD}, a floating-point unit for massively-parallel processors", journal = "Particle World", volume = "2", number = "3", pages = "65--73", month = "", year = "1991", CODEN = "PARWEG", ISSN = "1043-6790", bibdate = "Tue Dec 12 09:26:54 MST 1995", abstract = "The authors describe in detail the architecture and implementation of the MAD chip. It is a floating point unit, used as the elementary processing element of the APE100 array processor. The design has been accurately tailored to the requirements of a SIMD floating point intensive machine.", acknowledgement = ack-nhfb, affiliation = "Roma Univ., Italy", classification = "B1265F (Microprocessors and microcomputers); C5230 (Digital arithmetic methods); C5220P (Parallel architecture); C7320 (Physics and Chemistry); C5130 (Microprocessor chips)", keywords = "Floating-point unit; Massively-parallel processors; Architecture; Elementary processing element; APE100 array processor; SIMD floating point intensive machine", language = "English", pubcountry = "UK", thesaurus = "Digital arithmetic; Microprocessor chips; Parallel architectures; Physics computing", } @InProceedings{Bohlender:1991:SEF, author = "G. Bohlender and W. Walter and P. Kornerup and D. W. Matula", title = "Semantics for exact floating point operations", crossref = "Kornerup:1991:PIS", pages = "22--26", year = "1991", bibdate = "Wed Dec 13 13:13:34 MST 1995", note = "IEEE Catalog number 91CH3015-5.", abstract = "Semantics are given for the four elementary arithmetic operations and the square root, to characterize what are termed exact floating point operations. The operands of the arithmetic operations and the argument of the square root are all floating point numbers in one format. In every case, the result is a pair of floating point numbers in the same format with no accuracy lost in the computation. These semantics make it possible to realize the following principle: it shall be a user option to discard any information in the result of a floating point arithmetic operation. The reliability and portability previously associated with only mathematical software implementations in integer arithmetic can thus be attained exploiting the generally higher efficiency of floating point hardware.", acknowledgement = ack-nhfb, affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany", bookpages = "xiii + 282", classification = "C5230 (Digital arithmetic methods); C1160 (Combinatorial mathematics)", confdate = "26-28 June 1991", conflocation = "Grenoble, France", confsponsor = "IEEE; CNRS; IMAG", keywords = "Exact floating point operations; Elementary arithmetic operations; Square root; Operands; Argument; Floating point numbers; Semantics; Floating point arithmetic; Reliability; Portability; Mathematical software; Integer arithmetic; Floating point hardware", language = "English", pubcountry = "USA", thesaurus = "Digital arithmetic; Number theory", } @TechReport{Cody:1991:CPT, author = "W. J. Cody", title = "{CELEFUNT}: {A} Portable Test Package for Complex Elementary Functions", type = "Technical Report", number = "ANL-91/1", institution = inst-ANL, address = inst-ANL:adr, pages = "iii + 21", month = jan, year = "1991", bibdate = "Fri Sep 23 23:39:07 1994", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", acknowledgement = ack-nhfb, } @Article{Dritz:1991:IPS, author = "Kenneth W. Dritz", title = "Introduction to the proposed standard for the elementary functions in {Ada}", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "3--8", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C7310 (Mathematics)", corpsource = "Dept. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", keywords = "Ada; committees; elementary functions; generic package; ISO standard; mathematics computing; secondary; standards", treatment = "P Practical", } @Article{Dritz:1991:PSGa, author = "K. W. Dritz", title = "Proposed standard for a generic package of elementary functions for {Ada}", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "9--46", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C6110B (Software engineering techniques); C7310 (Mathematics)", corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", keywords = "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics Working Group; basic; elementary functions; ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package; GENERIC-ELEMENTARY-FUNCTIONS; Group; international standard; joint proposal; mathematical routines; mathematics computing; NRG; Rapporteur Group; reusable applications; SC22; software reusability; specification; standards; WG9 Numerics", treatment = "P Practical", } @Article{Dritz:1991:PSGb, author = "K. W. Dritz", title = "Proposed standard for a generic package of primitive functions for {Ada}", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "66--82", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C7310 (Mathematics)", corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", keywords = "Ada; compliable Ada; elementary functions; generic package; GENERIC-; mathematical; mathematics computing; primitive functions; primitive operations; PRIMITIVE-FUNCTIONS; software; specification; standards", treatment = "P Practical", } @Article{Dritz:1991:RPS, author = "K. W. Dritz", title = "Rationale for the proposed standard for a generic package of elementary functions for {Ada}", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "47--65", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C7310 (Mathematics); C6110 (Systems analysis and programming)", corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-Europe Numerics; collateral; elementary functions standard; mathematics computing; numerical software; portability; programming; robustness; standards; Working Group", treatment = "P Practical", } @Article{Duprat:1991:WND, author = "J. Duprat and J.-M. Muller", title = "Writing numbers differently for faster calculation", journal = j-TECHNIQUE-SCI-INFORMATIQUES, volume = "10", number = "3", pages = "211--224", month = "", year = "1991", CODEN = "TTSIDJ", ISSN = "0752-4072", bibdate = "Tue Dec 12 09:20:21 MST 1995", abstract = "Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.", acknowledgement = ack-nhfb, affiliation = "Ecole Normale Superieure de Lyon, France", classification = "C5230 (Digital arithmetic methods)", keywords = "Floating point arithmetic; Carry save methods; Borrow save; Addition; Subtraction; Shifting; Multiplication; Zero; Pseudo normalisation; Cordic algorithm", language = "French", pubcountry = "France", thesaurus = "Digital arithmetic", } @InProceedings{Ferguson:1991:AMA, author = "W. E. {Ferguson, Jr.} and T. Brightman", title = "Accurate and Monotone Approximations of Some Transcendental Functions", crossref = "Kornerup:1991:PIS", pages = "237--244", year = "1991", bibdate = "Sat Nov 27 12:40:58 MST 2004", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://ieeexplore.ieee.org/", acknowledgement = ack-nj # " and " # ack-nhfb, } @Article{Gal:1991:AEM, author = "Shmuel Gal and Boris Bachelis", title = "An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard", journal = j-TOMS, volume = "17", number = "1", pages = "26--45", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65-04 65D15)", MRnumber = "92a:65069", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html", abstract = "The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values. \par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.", } @InProceedings{Markstein:1991:WFF, author = "V. Markstein and P. Markstein and T. Nguyen and S. Poole", title = "Wide Format Floating-Point Math Libraries", crossref = "IEEE:1991:PSA", pages = "130--138", year = "1991", bibdate = "Wed Dec 13 18:34:51 1995", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", abstract = "The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett-Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliation = "ISQUARE, Inc., Austin, TX, USA", classification = "C5230 (Digital arithmetic methods); C5470 (Performance evaluation and testing); C7310 (Mathematics)", confdate = "18-22 Nov. 1991", conflocation = "Albuquerque, NM, USA", confsponsor = "IEEE; ACM", keywords = "Wide format floating point math libraries; Performance; Accuracy evaluations; Transcendental functions; Floating-point formats; Math libraries; Cray Y-MP; IBM 3090E/VF; Convex C-240; Hewlett-Packard 9000/720; IBM System/6000; 64 Bit; 128 Bit", language = "English", numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit", pubcountry = "USA", thesaurus = "Digital arithmetic; Mathematics computing; Parallel processing; Performance evaluation", } @Article{Midy:1991:CSE, author = "P. Midy and Y. Yakovlev", title = "Computing some elementary functions of a complex variable", journal = j-MATH-COMP-SIM, volume = "33", number = "1", pages = "33--49", year = "1991", CODEN = "MCSIDR", ISSN = "0378-4754", MRclass = "65Y10 (65D20)", MRnumber = "MR1122989", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, fjournal = "Mathematics and Computers in Simulation", } @Article{OGrady:1991:HOA, author = "E. Pearse O'Grady and Baek-Kyu Young", title = "A hardware-oriented algorithm for floating-point function generation", journal = j-IEEE-TRANS-COMPUT, volume = "40", number = "2", pages = "237--241", month = feb, year = "1991", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 08:40:52 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read/write memories illustrates the algorithm.", acknowledgement = ack-nhfb, } @Article{Okabe:1991:LDC, author = "Y. Okabe and N. Takagi and S. Yaima", key = "OTY91", title = "Log-Depth Circuits for Elementary Functions Using Residue Number System", journal = "Electronics and Communications in Japan", volume = "74", number = "8", pages = "31--37", year = "1991", bibdate = "Mon May 19 15:16:09 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz", note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728", acknowledgement = ack-nhfb, } @Book{Saan:1991:VFP, author = "T. Saan", title = "{\cyr Vychislenie {\`e}lementarnykh funktsi{\u{\i}}s pomoshch'yu drobno-ratsional'nykh priblizheni{\u{\i}}}. ({Russian}) [Calculation of elementary functions by means of rational approximations]", publisher = "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl. Tekhn. Inform., Tartu,", pages = "139", year = "1991", MRclass = "65-04 (65D15)", MRnumber = "94f:65008", MRreviewer = "W. Govaerts", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Smith:1991:AFP, author = "David M. Smith", title = "Algorithm 693: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic", journal = j-TOMS, volume = "17", number = "2", pages = "273--283", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html", abstract = "FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.", acknowledgement = ack-nhfb, affiliation = "Loyola Marymount Univ., Los Angeles, CA, USA", classification = "C7310 (Mathematics); C5230 (Digital arithmetic methods); C4130 (Interpolation and function approximation)", keywords = "Algorithms; Rounding off; Accuracy; Mathematical library; Portable software; Floating-point multiple-precision arithmetic; FM; FORTRAN-77 routines; Elementary functions", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", thesaurus = "Digital arithmetic; Function approximation; Mathematics computing; Software packages; Subroutines", } @Article{Squire:1991:ANS, author = "Jon S. Squire", title = "{Ada} numerics standardization and testing", journal = j-SIGADA-LETTERS, volume = "11", number = "7", address = "New York, NY, USA", pages = "1--286", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Sat Feb 24 15:01:45 MST 1996", acknowledgement = ack-nhfb, annote = "``A special edition from SIGAda \ldots{} presented by SIGAda Numerics Working Group and Ada-Europe Numerics Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics Rapporteur Group.''--Cover. Includes bibliographies. Introduction to the proposed standard for the elementary functions in Ada / Kenneth W. Dritz --- Proposed standard for a generic package of elementary functions for Ada / edited by Kenneth W. Dritz --- Rationale for the proposed standard for a generic package of elementary functions for Ada; Proposed standard for a generic package of primitive functions for Ada; Rationale for the proposed standard for a generic package of primitive functions for Ada / Kenneth W. Dritz --- Proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / edited by Graham S. Hodgson --- Rationale for the proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / Graham S. Hodgson. Proposed standard for a generic package of complex elementary functions / edited by Jon S. Squire --- Rationale for the proposed standard for a generic package of complex elementary functions / Jon S. Squire --- A portable generic elementary function package in Ada and an accurate test suite / Ping Tak Peter Tang --- Towards validation of generic elementary functions and other standard Ada numerics packages / Jon S. Squire --- Floating point attributes in Ada / Dik T. Winter --- An Ada math library for real-time avionics / Donald A. Celarier and Donald W. Sando --- Predifined floating point type names, uniformity rapporteur group UI-48 / edited by Jon S. Squire.", keywords = "Ada (Computer program language)", } @Article{Squire:1991:PSG, author = "J. S. Squire", title = "Proposed standard for a generic package of complex elementary functions (Ada)", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "140--165", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)", keywords = "ACM SIGAda; Ada; Ada-Europe Numerics Working Group; applications; complex elementary functions; complex mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS; generic package; GENERIC-; international standard; joint proposal; mathematics computing; Numerics Working Group; portable; reusable; software reusability; standards; WG9 Numerics Rapporteur Group", treatment = "P Practical", } @Article{Squire:1991:RPS, author = "J. S. Squire", title = "Rationale for the proposed standard for a generic package of complex elementary functions (Ada)", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "166--179", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)", keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-; basic complex mathematical; complex; COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions; error bounds; Europe Numerics Working Group; generic package; GENERIC-; mathematics computing; proposed standard; reusable applications; routines; software reusability; specification; standards", treatment = "P Practical", } @Article{Squire:1991:TVG, author = "J. S. Squire", title = "Towards validation of generic elementary functions and other standard {Ada} numerics packages", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "217--243", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6150G (Diagnostic, testing, debugging and evaluating systems); C7310 (Mathematics); C6140D (High level languages)", keywords = "Ada; Ada listings; computing; conformance testing; conformance tests; generic elementary functions; implementors guide; mathematics; program testing; proposed ISO; prototype tests; standard Ada numerics packages; standards; test suite", treatment = "P Practical", } @Article{Tang:1991:PGE, author = "Ping Tak Peter Tang", title = "A portable generic elementary function package in {Ada} and an accurate test suite", journal = j-SIGADA-LETTERS, volume = "11", number = "7", pages = "181--216", month = "Fall", year = "1991", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C6140D (High level languages); C6110B (Software engineering techniques); C6150G (Diagnostic, testing, debugging and evaluating systems)", keywords = "accurate test; Ada; function libraries; mathematics computing; portability; portable generic elementary function package; program testing; resolution; rigorous analysis; software; suite; test programs", treatment = "P Practical", } @InProceedings{Tang:1991:TLA, author = "Ping Tak Peter Tang", title = "Table-Lookup Algorithms for Elementary Functions and Their Error Analysis", crossref = "Kornerup:1991:PIS", pages = "232--236", year = "1991", bibdate = "Sat Nov 27 12:40:58 MST 2004", bibsource = "http://ieeexplore.ieee.org/; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nj # " and " # ack-nhfb, } @InProceedings{Wong:1991:FHA, author = "W. F. Wong and E. Goto", title = "Fast Hardware-based Algorithms for Elementary Function Computations", crossref = "Anonymous:1991:PIS", pages = "56--65", year = "1991", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, searchkey = "ti:elementary function", } @Article{Ziv:1991:FEE, author = "Abraham Ziv", title = "Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit", journal = j-TOMS, volume = "17", number = "3", pages = "410--423", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Sep 1 10:15:31 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html", acknowledgement = ack-nj, keywords = "algorithms; standardization; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Book{Baker:1992:CMF, author = "Louis Baker", title = "{C} mathematical function handbook", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xviii + 757", year = "1992", ISBN = "0-07-911158-0", ISBN-13 = "978-0-07-911158-6", LCCN = "QA351.B17 1991; QA351 .B17 1992", bibdate = "Fri Aug 31 18:54:02 MDT 2007", bibsource = "melvyl.cdlib.org:210/CDL90", series = "McGraw-Hill programming tools for scientists and engineers", acknowledgement = ack-nhfb, remark = "System requirements for computer disk: PC; C or C++ compiler.", subject = "Functions, Special; Computer programs; C (Computer program language)", } @Article{Baker:1992:LCE, author = "H. G. Baker", title = "Less Complex Elementary Functions", journal = j-SIGPLAN, volume = "27", number = "11", pages = "15--16", month = nov, year = "1992", CODEN = "SINODQ", ISSN = "0362-1340", bibdate = "Thu Sep 08 08:11:27 1994", acknowledgement = ack-nj, } @Article{Bohman:1992:FRP, author = "Jan Bohman and Carl-Erik Fr{\"o}berg", title = "The ${\Gamma}$-function revisited: power series expansions and real-imaginary zero lines", journal = j-MATH-COMPUT, volume = "58", number = "197", pages = "315--322", month = jan, year = "1992", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33B15 (11Y70 65D20)", MRnumber = "92e:33001", MRreviewer = "A. de Castro Brzezicki", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Dubois:1992:CFQ, author = "D. Dubois and H. Prade", title = "Calculation with fuzzy quantities", crossref = "EC2:1992:DJN", pages = "24--27", year = "1992", bibdate = "Thu Dec 14 17:22:18 MST 1995", abstract = "In some instances where numerical data are either provisional, incomplete, or variable within a limited range, the classical calculation of confidence intervals can be extended in a fuzzy-set approach, distinguishing between more or less plausible values. The simultaneous use of relatively wide intervals containing all possible values, and generally much narrower intervals covering only the most likely ones, can give sufficiently informative results. Some precautions advisable in arithmetic operations on imprecisely known quantities are outlined. Examples of application include provisional budgeting, resource estimation, evaluation of candidates, and extension of PERT to projects involving precedence among elementary tasks with uncertain durations and/or starting times. Computer-aided engineering design can also benefit from fuzzy specifications for values eventually to be optimised.", acknowledgement = ack-nhfb, affiliation = "IRIT, Paul Sabatier Univ., Toulouse, France", bookpages = "384", classification = "C7310 (Mathematics); C1160 (Combinatorial mathematics); C4210 (Formal logic)", confdate = "2-3 Nov. 1992", conflocation = "Nimes, France", keywords = "Fuzzy quantities; Numerical data; Confidence intervals; Fuzzy-set approach; Arithmetic operations; Imprecisely known quantities; Provisional budgeting; Resource estimation; Candidates; PERT; Engineering design; Fuzzy specifications", language = "French", pubcountry = "France", thesaurus = "Fuzzy logic; Fuzzy set theory; Statistical analysis", } @Article{Feinsilver:1992:BFR, author = "P. Feinsilver and R. Schott", title = "On {Bessel} functions and rate of convergence of zeros of {Lommel} polynomials", journal = j-MATH-COMPUT, volume = "59", number = "199", pages = "153--156", month = jul, year = "1992", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33C10 (33C45)", MRnumber = "93a:33007", MRreviewer = "Boro D{\"o}ring", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, affiliation = "Southern Illinois Univ., Carbondale, IL, USA", classcodes = "B0220 (Analysis); B0290P (Differential equations); B0290F (Interpolation and function approximation); B0210 (Algebra); C1120 (Analysis); C4170 (Differential equations); C4130 (Interpolation and function approximation); C1110 (Algebra)", classification = "B0210 (Algebra); B0220 (Analysis); B0290F (Interpolation and function approximation); B0290P (Differential equations); C1110 (Algebra); C1120 (Analysis); C4130 (Interpolation and function approximation); C4170 (Differential equations)", corpsource = "Southern Illinois Univ., Carbondale, IL, USA", keywords = "average case analysis; Average case analysis; Bessel function; Bessel functions; convergence of numerical methods; convergence rate; Convergence rate; data structures; differential equations; dynamic; Dynamic data structures; Lommel; Lommel polynomials; Maple program; polynomials; rate of convergence; Rate of convergence; zeros; Zeros", thesaurus = "Bessel functions; Convergence of numerical methods; Differential equations; Polynomials", treatment = "T Theoretical or Mathematical", } @Article{Kearfott:1992:IPF, author = "Baker Kearfott and Milind Dawande and Kaisheng Du and Chen-Yi Hu", title = "{INTLIB}: {A} Portable {FORTRAN} 77 Elementary Function Library", journal = j-INTERVAL-COMP, volume = "3", number = "5", pages = "96--105", year = "1992", ISSN = "0135-4868", MRclass = "65G10", MRnumber = "1 253 132", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", note = "Interval '92 (Moscow, 1992).", acknowledgement = ack-nhfb, } @Article{Lang:1992:HRS, author = "T. Lang and P. Montuschi", title = "Higher radix square root with prescaling", journal = j-IEEE-TRANS-COMPUT, volume = "41", number = "8", pages = "996--1009", month = aug, year = "1992", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A scheme for performing higher radix square root based on prescaling of the radicand is presented to reduce the complexity of the result-digit selection. The scheme requires several steps, namely multiplication for prescaling the radicand, square \ldots{}", } @Article{McQuillan:1992:VMH, author = "S. E. McQuillan and J. V. McCanny", title = "{VLSI} module for high-performance multiply, square root and divide", journal = j-IEE-PROC-COMPUT-DIGIT-TECH, volume = "139", number = "6", pages = "505--510", month = nov, year = "1992", CODEN = "ICDTEA", ISSN = "1350-2387", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A high-performance VLSI architecture to perform multiply-accumulate, division and square root operations is proposed. The circuit is highly regular, requires only minimal control and ean be pipelined right down to the bit level. The system can also \ldots{}", } @Article{Mikami:1992:NDO, author = "N. Mikami and M. Kobayashi and Y. Yokoyama", title = "A New {DSP}-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter", journal = j-IEEE-TRANS-SIG-PROC, volume = "40", number = "7", pages = "1663--1669", month = jul, year = "1992", CODEN = "ITPRED", ISSN = "1053-587X", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://ieeexplore.ieee.org/", acknowledgement = ack-nj # " and " # ack-nhfb, summary = "A high-speed algorithm for calculating the square root is proposed. This algorithm, which can be regarded as calculation of the step response of a kind of nonlinear IIR filter, requires no divisions. Therefore, it is suitable for a VLSI digital \ldots{}", } @Article{Mitchell:1992:VFA, author = "H. B. Mitchell", title = "Very fast accurate square-root algorithm for use with gradient edge operators", journal = j-ELECT-LETTERS, volume = "28", number = "10", pages = "922--923", day = "7", month = may, year = "1992", CODEN = "ELLEAK", ISSN = "0013-5194", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Commonly used gradient edge operators such as the Sobel, Prewitt and Roberts operators all required a square root operation; this is, however, computationally intensive and, consequently, simple but very inaccurate approximations are often used \ldots{}", } @Article{Salwin:1992:UPE, author = "A. E. Salwin", title = "Using the Proposed Elementary Functions Standard to Build a Strongly Typed Trig Package", journal = j-SIGADA-LETTERS, volume = "12", number = "5", pages = "59--63", month = sep # "\slash " # oct, year = "1992", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Thu Mar 20 07:41:09 MST 1997", acknowledgement = ack-nhfb, classcodes = "C6140D (High level languages)", corpsource = "Mitre Corp., McLean, VA, USA", keywords = "Ada; compiler; elementary functions standard; standards; strong typing; strongly typed trig package; trigonometric functions", treatment = "P Practical", } @MastersThesis{Schulte:1992:AHD, author = "Michael Joseph Schulte and Function generation", title = "Algorithms and hardware designs for parallel elementary function generation", type = "Thesis (M.S. in Engin.)", school = "University of Texas at Austin", address = "Austin, TX, USA", pages = "ix + 73", year = "1992", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, keywords = "Computer science -- Mathematics.; Numerical analysis.; Computer input-output equipment -- Design and construction.; Parallel processing (Electronic computers)", searchkey = "ti:elementary n1 function", } @Article{Tang:1992:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Expm1 Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "18", number = "2", pages = "211--222", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15", MRnumber = "1 167 891", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/; http://doi.acm.org/10.1145/146847.146928", abstract = "Algorithms and implementation details for the function $e^x - 1$ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Temme:1992:AII, author = "N. M. Temme", title = "Asymptotic Inversion of Incomplete Gamma Functions", journal = j-MATH-COMPUT, volume = "58", number = "198", pages = "755--764", month = apr, year = "1992", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33B20", MRnumber = "93a:33003", MRreviewer = "F. W. J. Olver", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Wong:1992:DSR, author = "W. F. Wong and E. Goto", title = "Division and square-rooting using a split multiplier", journal = j-ELECT-LETTERS, volume = "28", number = "18", pages = "1758--1759", day = "27", month = aug, year = "1992", CODEN = "ELLEAK", ISSN = "0013-5194", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A modification is proposed to the traditional design of a fast floating point multiplication circuit such that instead of just performing A$\times$B where A and B are m bits long, it is also capable of \ldots{}", } @InProceedings{Woods:1992:HPD, author = "R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny", booktitle = "Proceedings of Fifth Annual IEEE International ASIC Conference and Exhibit, 1992", title = "High performance {DSP} {ASIC} for multiply, divide and square root", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "209--213", year = "1992", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The design of a high-speed ASIC that combines the operations of multiplication, division and square root is described. The chip is based on a systolic array architecture that uses a redundant number system and allows multiplication, division, and \ldots{}", } @Article{Alzer:1993:SGF, author = "Horst Alzer", title = "Some gamma function inequalities", journal = j-MATH-COMPUT, volume = "60", number = "201", pages = "337--346", month = jan, year = "1993", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33B15 (26D20)", MRnumber = "93f:33001", MRreviewer = "Aurelio Cannizzo", bibdate = "Sat Jan 11 13:29:06 MST 1997", acknowledgement = ack-nhfb, } @Article{Bailey:1993:AMT, author = "D. H. Bailey", title = "Algorithm 719: Multiprecision Translation and Execution of {FORTRAN} Programs", journal = j-TOMS, volume = "19", number = "3", pages = "288--319", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Dec 13 18:37:31 1995", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", abstract = "The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA", classification = "C7310 (Mathematics); C5230 (Digital arithmetic methods); C6140D (High level languages); C6150C (Compilers, interpreters and other processors); C6120 (File organisation)", keywords = "Algorithm 719; Multiprecision translation; Fortran programs; Fortran utilities; Multiprecision computation; Fortran subroutines; Arithmetic operations; Transcendental functions; Floating point numbers; Translator program; Source directives; Multiprecision subroutine calls; Complex data types; Array space; Computational expressions; Operator precedence; Mixed mode operations; Fortran-77 intrinsics; Multiprecision data types", language = "English", pubcountry = "USA", thesaurus = "Data structures; Digital arithmetic; FORTRAN; Mathematics computing; Program interpreters; Subroutines", } @InCollection{Bohlender:1993:PAF, author = "G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter", title = "Proposal for accurate floating-point vector arithmetic", crossref = "Adams:1993:ACA", pages = "87--102", year = "1993", bibdate = "Tue Dec 12 09:27:13 MST 1995", abstract = "Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.", acknowledgement = ack-nhfb, affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany", bookpages = "x + 612", classification = "C5230 (Digital arithmetic methods); C7310 (Mathematics); C6130 (Data handling techniques)", keywords = "Floating point numbers; Elementary floating-point operations; IEEE standards; IEEE arithmetic; Numerical algorithms; Compound operations; Summation; Sequence; Dot product; Rounding errors; Catastrophic cancellation; Leading digits; Standards; Vector operations; Elementary scalar arithmetic operations; Rounding modes; Accuracy requirements; Data formats; Operands; Scalar floating-point arithmetic", language = "English", pubcountry = "USA", thesaurus = "Digital arithmetic; Mathematics computing; Roundoff errors; Standards", } @Article{Cody:1993:ACP, author = "W. J. Cody", title = "Algorithm 714: {CELEFUNT}: {A} Portable Test Package for Complex Elementary Functions", journal = j-TOMS, volume = "19", number = "1", pages = "1--21", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://www.acm.org/pubs/toc/Abstracts/toms/151272.html", abstract = "This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.", acknowledgement = ack-nhfb, affiliation = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", classification = "C7310 (Mathematics); C5230 (Digital arithmetic methods); C4100 (Numerical analysis)", keywords = "CELEFUNT; Portable test package; Complex elementary functions; Fortran programs; Floating-point elementary functions; CABS; CSQRT; CLOG; CEXP; CSIN/CCOS; Complex power function; algorithms; measurement; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", thesaurus = "Conformance testing; Digital arithmetic; FORTRAN; Mathematics computing; Numerical analysis; Program testing; Software packages", } @Article{Frappier:1993:QFI, author = "Cl{\'e}ment Frappier and Patrick Olivier", title = "A quadrature formula involving zeros of {Bessel} functions", journal = j-MATH-COMPUT, volume = "60", number = "201", pages = "303--316", month = jan, year = "1993", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "41A55 (65D32)", MRnumber = "93d:41025", MRreviewer = "Hans Strauss", bibdate = "Tue Mar 25 15:38:13 MST 1997", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); B0290M (Numerical integration and differentiation); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. de Math. Appliqu{\'e}es, Montreal, Que., Canada", keywords = "Bessel functions; integration; interpolation; poles and; polynomials; quadrature formula; sampling theorem; zeros", treatment = "T Theoretical or Mathematical", } @Article{Hu:1993:BRS, author = "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad", title = "On Bounding the Range of Some Elementary Functions in {FORTRAN} 77", journal = j-INTERVAL-COMP, volume = "1993", number = "3", pages = "29--39", year = "1993", ISSN = "0135-4868", MRclass = "65G10", MRnumber = "1 305 844", bibdate = "Wed Dec 4 11:13:33 1996", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", note = "Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)", acknowledgement = ack-nhfb, } @TechReport{Litvinov:1993:ACR, author = "Grigori L. Litvinov", title = "Approximate construction of rational approximations and the effect of error autocorrection", type = "Technical report", number = "8", institution = "Institute of Mathematics, University of Oslo", address = "Oslo, Norway", month = may, year = "1993", bibdate = "Tue Mar 24 20:51:52 2009", note = "See \cite{Litvinov:1994:ACR}.", acknowledgement = ack-nhfb, } @Article{Liu:1993:DSC, author = "Hui Min Liu", title = "Determination of several classes of elementary functions by functional inequalities. (Chinese)", journal = "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)", volume = "11", number = "2", pages = "30--35, 12", year = "1993", ISSN = "1001-6074", MRclass = "26A09 (39B72)", MRnumber = "94g:26003", MRreviewer = "Ling Yau Chan", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Louie:1993:DRS, author = "M. E. Louie and M. D. Ercegovac", booktitle = "Proceedings of the IEEE Workshop on FPGAs for Custom Computing Machines, 5--7 April 1993", title = "A digit-recurrence square root implementation for field programmable gate arrays", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "178--183", year = "1993", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Creating efficient arithmetic processors requires a pairing of high speed arithmetic algorithms with optimal mapping strategies for a given technology. The authors propose bit reduction as key to an efficient pairing process for lookup table based \ldots{}", } @InProceedings{Lozier:1993:ABF, author = "Daniel W. Lozier and F. W. J. Olver", title = "{Airy} and {Bessel} Functions by Parallel Integration of {ODEs}", crossref = "Sincovec:1993:PSS", pages = "530--538", year = "1993", bibdate = "Fri Jul 09 06:36:27 2004", acknowledgement = ack-nhfb, } @InProceedings{McQuillan:1993:NAV, author = "S. E. McQuillan and J. V. McCanny and R. Hamill", booktitle = "Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993", title = "New algorithms and {VLSI} architectures for {SRT} division and square root", crossref = "Swartzlander:1993:SCA", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "80--86", year = "1993", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-sfo # " and " # ack-nhfb, summary = "Radix two algorithms for SRT division and square-rooting are developed. For these schemes, the result digits and the residuals are computed concurrently and the computations in adjacent rows are overlapped. Consequently, their performance should \ldots{}", } @Article{Montuschi:1993:RIT, author = "P. Montuschi and L. Ciminiera", title = "Reducing iteration time when result digit is zero for radix $2$ {SRT} division and square root with redundant remainders", journal = j-IEEE-TRANS-COMPUT, volume = "42", number = "2", pages = "239--246", month = feb, year = "1993", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", note = "See remark \cite{Montuschi:1995:RRI}.", acknowledgement = ack-sfo # " and " # ack-nhfb, summary = "A new architecture is presented for shared radix 2 division and square root whose main characteristic is the ability to avoid any addition/subtraction, when the digit 0 has been selected. The solution presented uses a redundant representation of the \ldots{}", } @Book{Povolotskii:1993:OFR, author = "A. I. Povolotski{\u{\i}} and G. A. Sviridyuk", title = "{\cyr Odnomerny{\u{\i}}matematicheski{\u{\i}}analiz {\`e}lementarnykh funktsi{\u{\i}}}. ({Russian}) [One-dimensional mathematical analysis of elementary functions] {\cyr Nepreryvnye funktsii. Differentsiruemye funktsii. Integriruemye funktsii}. [Continuous functions. Differentiable functions. Integrable functions]", publisher = "Chelyabinsk. Gos. Univ.", address = "Chelyabinsk, USSR", pages = "92", year = "1993", ISBN = "5-230-17764-0", ISBN-13 = "978-5-230-17764-7", MRclass = "26-01 (00A05)", MRnumber = "94e:26001", MRreviewer = "J{\'o}zef Kalinowski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Schulte:1993:ERC, author = "M. Schulte and E. Swartzlander", title = "Exact rounding of certain elementary functions", crossref = "Swartzlander:1993:SCA", pages = "138--145", year = "1993", bibdate = "Thu Dec 14 11:25:18 MST 1995", URL = "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf", abstract = "An algorithm is described which produces exactly rounded results for the functions of reciprocal, square root, 2/sup x/, and log 2/sup x/. Hardware designs based on this algorithm are presented for floating point numbers with 16- and 24-b significands. These designs use a polynomial approximation in which coefficients are originally selected based on the Chebyshev series approximation and are then adjusted to ensure exactly rounded results for all inputs. To reduce the number of terms in the approximation, the input interval is divided into subintervals of equal size and different coefficients are used for each subinterval. For floating point numbers with 16-b significands, the exactly rounded value of the function can be computed in 51 ns on a 20-mm/sup 2/ chip. For floating point numbers with 24-b significands, the functions can be computed in 80 ns on a 98-mm/sup 2/ chip.", acknowledgement = ack-nhfb, affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA", bookpages = "xii + 284", classification = "C4120 (Functional analysis); C5230 (Digital arithmetic methods)", confdate = "29 June--2 July 1993", conflocation = "Windsor, Ont., Canada", confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI; Natural Sci. and Eng. Res.; Council of Canada", keywords = "Elementary functions; Exact rounding; Floating point numbers; Polynomial approximation; Reciprocal; Rounded results; Square root", thesaurus = "Floating point arithmetic; Function evaluation", } @Article{Schulte:1993:PHD, author = "Michael J. Schulte and Earl E. {Swartzlander, Jr.}", title = "Parallel hardware designs for correctly rounded elementary functions", journal = j-INTERVAL-COMP, volume = "4", pages = "65--88", year = "1993", ISSN = "0135-4868", MRclass = "65G10 (65C20)", MRnumber = "1 305 859", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)", acknowledgement = ack-nhfb, } @TechReport{Schwarz:1993:HRAa, author = "E. Schwarz", title = "High-radix algorithms for high-order arithmetic operations", type = "Technical Report", number = "CSL-TR-93-559", institution = "Computer Systems Laboratory, Stanford University", address = "Stanford, CA, USA", month = jan, year = "1993", bibdate = "Thu Apr 2 08:38:35 1998", acknowledgement = ack-sfo # " and " # ack-nhfb, } @PhdThesis{Schwarz:1993:HRAb, author = "Eric Mark Schwarz", title = "High-radix algorithms for high-order arithmetic operations", type = "Thesis ({Ph.D.})", school = "Department of Electrical Engineering, Stanford University", address = "Stanford, CA, USA", pages = "224", month = apr, year = "1993", bibdate = "Mon Jan 07 22:38:06 2008", abstract = "Many common algorithms for high-order arithmetic operations require an initial approximation. The Newton-Raphson algorithm starts with an approximation and then quadratically converges on the solution. The initial approximation determines the number of iterations of the algorithm and is typically implemented as a look-up table in the form of a ROM or PLA. A novel method is suggested which describes high-order arithmetic operations with a partial product array. This method applies to the operations of division, reciprocal, square root, natural logarithm, exponential, and trigonometric functions. The partial product array of Boolean elements which describes the operation can be summed on an existing floating-point multiplier. The hardware needed is only the logic gates to create the Boolean elements in the array and a multiplexor, and the latency is that of the multiplier. Thus, by reusing a floating-point multiplier, a high-precision approximation to a high-order arithmetic operation can be implemented with a low marginal cost.\par This dissertation describes the implementation and shows a method for deriving partial product arrays to approximate arithmetic operations. Then the proposed method is applied and evaluated for several operations. The proposed method yields a minimum approximation of twelve bits correct for the reciprocal operation and sixteen bits for the square root operation. The proposed method is shown to be as small as 0.05\% the size (in gates) of an equivalent precision look-up table and has up to four times the accuracy (in bits) as an equivalent latency polynomial approximation. Also, three new iterative algorithms to increase the precision of the approximations and a theoretical analysis of the partial product array representation are detailed. Thus, high-radix algorithms of many arithmetic operations are possible at low cost.", acknowledgement = ack-nhfb, keywords = "division; elementary functions; exponential; logarithm; PPA (partial product array); reciprocal square root; square root", remark = "AAT 9317816. ProQuest document ID 746798521.", } @InProceedings{Schwarz:1993:HSA, author = "E. M. Schwarz and M. J. Flynn", booktitle = "Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993", title = "Hardware starting approximation for the square root operation", crossref = "Swartzlander:1993:SCA", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "103--111", year = "1993", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-sfo # " and " # ack-nhfb, summary = "A method for obtaining high-precision approximations of high-order arithmetic operations is presented. These approximations provide an accurate starting approximation for high-precision iterative algorithms, which translates into few iterations and \ldots{}", } @Article{Shishkov:1993:RDB, author = "Dimit{\cdprime}r Shishkov", title = "Reduction of domains of basic elementary functions to arbitrary small intervals", journal = "Annuaire Univ. Sofia Fac. Math. Inform.", volume = "87", number = "1-2", pages = "3--32 (1999)", year = "1993", ISSN = "0205-0808", MRclass = "65D20", MRnumber = "MR1745336", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment Okhridski''. Fakultet po Matematika i Informatika. Annuaire de l'Universit\'e de Sofia ``St. Kliment Ohridski''. Facult\'e de Math\'ematiques et Informatique", } @Article{Anonymous:1994:C, author = "Anonymous", title = "Corrigenda", journal = j-TOMS, volume = "20", number = "4", pages = "553--553", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:03 1995", note = "See \cite{Hull:1994:ICE}", acknowledgement = ack-rfb, } @Article{Bajard:1994:BNH, author = "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel Muller", title = "{BKM}: a new hardware algorithm for complex elementary functions", journal = j-IEEE-TRANS-COMPUT, volume = "43", number = "8", pages = "955--963", year = "1994", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "68M07", MRnumber = "1 294 301", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Chen:1994:EDU, author = "Sau-Gee Chen and Chieh-Chih Li", booktitle = "Proceedings of TENCON '94. IEEE Region 10's Ninth Annual International Conference. Theme: `Frontiers of Computer Technology'", title = "Efficient designs of unified $2$'s complement division and square root algorithm and architecture", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "943--947", year = "1994", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Efficient unified 2's complement division and square root algorithm, and their architectures are proposed in this work. The designs are high speed, small area and high compatibility. The architectures provide bit level pipelined operation, as well \ldots{}", } @Article{Cortadella:1994:HRD, author = "J. Cortadella and T. Lang", title = "High-Radix Division and Square-Root with Speculation", journal = j-IEEE-TRANS-COMPUT, volume = "43", number = "8", pages = "919--931", month = aug, year = "1994", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/; OCLC Proceedings database", acknowledgement = ack-sfo # " and " # ack-nhfb, remark = "Selected revised and extended papers from ARITH'11 \cite{Swartzlander:1993:SCA}.", summary = "The speed of high-radix digit-recurrence dividers and square-root units is mainly determined by the complexity of the result-digit selection. We present a scheme in which a simpler function speculates the result digit, and, when this speculation is \ldots{}", } @Article{Damnjanovic:1994:EFL, author = "Zlatan Damnjanovic", title = "Elementary functions and loop programs", journal = "Notre Dame J. Formal Logic", volume = "35", number = "4", pages = "496--522", year = "1994", CODEN = "NDJFAM", ISSN = "0029-4527", MRclass = "03D20 (68Q15)", MRnumber = "96i:03036", MRreviewer = "John P. Helm", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Das:1994:ATE, author = "Mrinal Kanti Das", title = "Analysis of two elementary functions", journal = j-INT-J-MATH-EDU-SCI-TECH, volume = "25", number = "1", pages = "17--24", year = "1994", CODEN = "IJMEBM", ISSN = "0020-739X", MRclass = "26-01 (33B10)", MRnumber = "1 257 731", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Dunham:1994:PMAa, author = "Charles B. Dunham", title = "Provably Monotone Approximations, {IV}", type = "Technical report", number = "TR-417", institution = "Department of Computer Science, University of Western Ontario", address = "London, Ontario, Canada", day = "8", month = mar, year = "1994", bibdate = "Tue Apr 12 11:26:47 2005", URL = "http://www.csd.uwo.ca/tech-reports/", acknowledgement = ack-nhfb, } @TechReport{Dunham:1994:PMAb, author = "Charles B. Dunham", title = "Provably Monotone Approximations, {IV}, Revised", type = "Technical report", number = "TR-422", institution = "Department of Computer Science, University of Western Ontario", address = "London, Ontario, Canada", day = "4", month = apr, year = "1994", bibdate = "Tue Apr 12 11:26:47 2005", URL = "http://www.csd.uwo.ca/tech-reports/", acknowledgement = ack-nhfb, } @Article{Hull:1994:ICE, author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang", title = "Implementing Complex Elementary Functions Using Exception Handling", journal = j-TOMS, volume = "20", number = "2", pages = "215--244", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 21 15:10:29 1995", note = "See \cite{Anonymous:1994:C}.", abstract = "Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).", acknowledgement = ack-nhfb, keywords = "algorithms; complex elementary functions; design; implementation", subject = "G.1.0 [Numerical Analysis]: General--error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation--elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software--algorithm analysis; reliability and robustness; verification", } @InProceedings{Jain:1994:SRR, author = "V. K. Jain and Lei Lin", booktitle = "IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP-94, 19--22 April 1994", title = "Square-root, reciprocal, sine\slash cosine, arctangent cell for signal and image processing", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "II/521--II/524", year = "1994", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "This paper discusses an efficient interpolation method for nonlinear function generation. Based on this, a 24 bit VLSI cell, capable of computing the (1) square root, (2) reciprocal, (3) sine/cosine, and (4) arctangent functions, is presented for \ldots{}", } @Article{Kearfott:1994:AIP, author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu", title = "Algorithm 737: {INTLIB}: {A} Portable {Fortran}-77 Elementary Function Library", journal = j-TOMS, volume = "20", number = "4", pages = "447--459", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat May 20 15:54:18 1995", accepted = "December 1993", acknowledgement = ack-rfb, keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic; operator overloading; standard functions", subject = "D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation", } @Article{Litvinov:1994:ACR, author = "Grigori L. Litvinov", title = "Approximate construction of rational approximations and the effect of error autocorrection", journal = j-RUSS-J-MATH-PHYS, volume = "1", number = "3", pages = "313--352", month = "????", year = "1994", CODEN = "RJMPEL", ISSN = "1061-9208", bibdate = "Tue Mar 24 20:54:11 2009", URL = "http://arxiv.org/abs/math/0101042", abstract = "Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pad{\'e} approximations, linear and nonlinear Pad{\'e} Chebyshev approximations) where very significant errors in the coefficients do not affect the accuracy of the approximation. The matter of import is that the errors in the numerator and the denominator of a fractional rational approximant compensate each other. This effect is related to the fact that the errors in the coefficients of a rational approximant are not distributed in an arbitrary way but form the coefficients of a new approximant to the approximated function. Understanding of the error autocorrection mechanism allows to decrease this error by varying the approximation procedure depending on the form of the approximant. Some applications are described in the paper. In particular, a method of implementation of basic calculations on decimal computers that uses the technique of rational approximations is described in the Appendix.\par To a considerable extent the paper is a survey and the exposition is as elementary as possible.", acknowledgement = ack-nhfb, } @InCollection{Lozier:1994:NES, author = "Daniel W. Lozier and F. W. J. Olver", title = "Numerical evaluation of special functions", crossref = "Gautschi:1994:MCH", volume = "48", pages = "79--125", year = "1994", MRclass = "65D20 (30-04 33-04 41-04)", MRnumber = "95m:65036", MRreviewer = "John P. Coleman", bibdate = "Fri Jul 9 05:44:10 2004", series = "Proc. Sympos. Appl. Math.", URL = "http://math.nist.gov/mcsd/Reports/2001/nesf/", abstract = "Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists, and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in the field.", acknowledgement = ack-nhfb, remark = "The references list contains about 400 entries which should ultimately be incorporated in this BibTeX bibliography collection.", } @TechReport{Lozier:1994:SNS, author = "Daniel W. Lozier", title = "Software Needs in Special Functions", type = "Technical Report", number = "NISTIR 5490", institution = pub-NIST, address = pub-NIST:adr, pages = "16", month = aug, year = "1994", bibdate = "Fri Jul 09 05:47:26 2004", note = "Published in \cite{Lozier:1996:SNS}.", URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps", acknowledgement = ack-nhfb, } @InProceedings{Magnus:1994:ASA, author = "Alphonse P. Magnus", title = "Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the `$1/9$' problem) by the {Carath{\'e}odory--Fej{\'e}r} method", crossref = "Cuyt:1994:NNM", pages = "173--185", year = "1994", bibdate = "Mon Nov 24 21:30:41 2008", acknowledgement = ack-nhfb, ZMnumber = "809.41015", } @Article{Merrheim:1994:CEF, author = "X. Merrheim", title = "The computation of elementary functions in radix $2^p$. International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)", journal = j-COMPUTING, volume = "53", number = "3--4", pages = "219--232", year = "1994", CODEN = "CMPTA2", ISSN = "0010-485X", MRclass = "68M07", MRnumber = "95j:68028", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Narayanaswami:1994:AE, author = "Chandrasekhar Narayanaswami and William Luken", title = "Approximating $x^n$ efficiently", journal = j-INFO-PROC-LETT, volume = "50", number = "4", pages = "205--210", day = "25", month = may, year = "1994", CODEN = "IFPLAT", ISSN = "0020-0190", MRclass = "65D20 (41-04 65B99)", MRnumber = "95b:65031", bibdate = "Wed Nov 11 12:16:26 MST 1998", bibsource = "Compendex database; http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/", acknowledgement = ack-nhfb, affiliation = "IBM Advanced Workstations and Systems Div", affiliationaddress = "Austin, TX, USA", classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation); C6130B (Graphics techniques)", corpsource = "IBM Adv. Workstations and Syst. Div., Austin, TX, USA", journalabr = "Inf Process Lett", keywords = "Approximation theory; approximation theory; $x^n$ approximation; Color computer graphics; Computational complexity; Computational methods; computer graphics; elementary functions; floating-point arithmetic; Function evaluation; graphics modeling; Image quality; Light intensity computation; look-up tables; performance requirements; Polynomial evaluation; Polynomials; polynomials; power function; scientific applications; Semiconducting silicon; Table lookup", treatment = "T Theoretical or Mathematical", } @Article{Nishioka:1994:EFB, author = "Keiji Nishioka", title = "Elementary functions based on elliptic curves", journal = j-TOKYO-J-MATH, volume = "17", number = "2", pages = "439--446", year = "1994", ISSN = "0387-3870", MRclass = "12H05", MRnumber = "96b:12011", MRreviewer = "Alexandru Buium", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Ohta:1994:INP, author = "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and Nobuaki Yoshida", title = "Improvement and new proposal on fast evaluation of elementary functions. (Japanese)", journal = "Transactions of the Information Processing Society of Japan", volume = "35", number = "5", pages = "926--933", month = may, year = "1994", CODEN = "JSGRD5", ISSN = "0387-5806", MRclass = "65D20", MRnumber = "95f:65045", bibdate = "Sat Jan 11 17:44:01 MST 1997", abstract = "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp. 1570-1579, 1993) introduced fast methods for numerical evaluation of elementary functions based on table lookup. They are called ATA (add/table-lookup/add) and ATA-M (add/table-lookup/add and multiply) methods for single- and double-precision calculations respectively. In this paper, an improvement to these methods that shrinks the size of the table by a factor of about 3/16 is presented. Another method called the `split parallel multiplication method', which is characterized by simpler table lookup than ATA-M and by split and parallel use of double-precision floating point circuitry, is also introduced, These new methods fit on to integrated circuits of a size comparable with commercially available floating-point accelerators. Methods for accelerating double-precision division, generating uniform pseudo-random numbers in double-precision, and accelerating the multiplication of single-precision complex numbers using the same circuitry are proposed.", acknowledgement = ack-nhfb, affiliation = "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan", classification = "C5230 (Digital arithmetic methods); C4120 (Functional analysis); C6130 (Data handling techniques)", keywords = "Elementary functions evaluation; Numerical evaluation; ATA method; Add/table-lookup/add method; ATA-M method; Add/table-lookup/add/multiply method; Single-precision calculations; Double-precision calculations; Table size; Split parallel multiplication method; Double-precision floating point circuitry; Integrated circuits; Floating-point accelerators; Double-precision division; Uniform pseudo-random number generation; Single-precision complex number multiplication", language = "Japanese", pubcountry = "Japan", thesaurus = "Digital arithmetic; Function evaluation; Random number generation; Table lookup", } @Article{Schulte:1994:HDE, author = "M. J. Schulte and E. E. {Swartzlander, Jr.}", title = "Hardware Design for Exactly Rounded Elementary Functions", journal = j-IEEE-TRANS-COMPUT, volume = "43", number = "8", pages = "964--973", month = aug, year = "1994", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Tue Dec 12 09:29:07 MST 1995", abstract = "This paper presents hardware designs that produce exactly rounded results for the functions of reciprocal, square-root, 2/sup x/, and log/sub 2/(x). These designs use polynomial approximation in which the terms in the approximation are generated in parallel, and then summed by using a multi-operand adder. To reduce the number of terms in the approximation, the input interval is partitioned into subintervals of equal size, and different coefficients are used for each subinterval. The coefficients used in the approximation are initially determined based on the Chebyshev series approximation. They are then adjusted to obtain exactly rounded results for all inputs. Hardware designs are presented, and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result. For single-precision floating point numbers, a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS technology. Allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5\% to 30\% and the area requirements by 33\% to 77\%.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA", classification = "B2570D (CMOS integrated circuits); B1265B (Logic circuits); B0290F (Interpolation and function approximation); C5230 (Digital arithmetic methods); C5120 (Logic and switching circuits); C4130 (Interpolation and function approximation)", keywords = "Hardware designs; Exactly rounded elementary functions; Reciprocal; Square-root; Polynomial approximation; Multi-operand adder; Chebyshev series approximation; Single-precision floating point numbers; Chip area; 1.0-Micron CMOS technology; Computational delay; Computer arithmetic; Exact rounding; Parallel multiplier; Argument reduction; Special-purpose hardware; 1 Micron", language = "English", numericalindex = "Size 1.0E-06 m", pubcountry = "USA", thesaurus = "Approximation theory; Chebyshev approximation; CMOS integrated circuits; Digital arithmetic; Multiplying circuits; Polynomials; Summing circuits", } @Article{Spouge:1994:CGD, author = "John L. Spouge", title = "Computation of the Gamma, Digamma, and Trigamma Functions", journal = j-SIAM-J-NUMER-ANAL, volume = "31", number = "3", pages = "931--944", month = jun, year = "1994", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", MRclass = "33B15 (30E10 33-04 40-04 65D20)", MRnumber = "95g:33002", MRreviewer = "E. Kaucher", bibdate = "Mon Jan 20 15:27:00 MST 1997", acknowledgement = ack-nhfb, } @Article{Timmermann:1994:CFV, author = "D. Timmermann and B. Rix and H. Hahn and B. J. Hosticka", title = "A {CMOS} floating-point vector-arithmetic unit", journal = j-IEEE-J-SOLID-STATE-CIRCUITS, volume = "29", number = "5", pages = "634--639", month = may, year = "1994", CODEN = "IJSCBC", ISSN = "0018-9200", bibdate = "Tue Dec 12 09:29:07 MST 1995", abstract = "This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 mu m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS.", acknowledgement = ack-nhfb, affiliation = "Fraunhofer Inst. of Microelectron. Circuits and Syst., Duisburg, Germany", classification = "B1265B (Logic circuits); B2570D (CMOS integrated circuits); C5230 (Digital arithmetic methods); C5120 (Logic and switching circuits); C5220P (Parallel architecture)", keywords = "Double-metal n-well CMOS technology; Floating-point vector-arithmetic unit; CORDIC algorithm; Multiplication; Division; Sine; Cosine; Hyperbolic sine; Square root; Natural logarithm; Inverse tangent; Vector norm; Phase; 1.6 Micron; 220 MFLOPS", language = "English", numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS", pubcountry = "USA", thesaurus = "CMOS integrated circuits; Digital arithmetic; Integrated logic circuits; Parallel architectures; Pipeline processing; Vector processor systems", } @Book{Watanabe:1994:MSP, author = "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu Oguni", title = "Mathematical Software for the {P.C.} and Work Stations: {A} Collection of {Fortran 77} Programs", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xiv + 387", month = jun, year = "1994", ISBN = "0-444-82000-0", ISBN-13 = "978-0-444-82000-6", LCCN = "QA 76.73 F25 F6813 1994", bibdate = "Sun Sep 28 10:42:07 MDT 1997", bibsource = "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/; http://www.cbooks.com/", note = "Translation of: FORTRAN 77 ni yoru suchi keisan sofutowea.", price = "US\$178.50", URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000", acknowledgement = ack-nhfb, alttitle = "{Fortran 77} ni yoru suchi keisan sofutowea. English.", keywords = "Fortran 77 (computer program language); Numerical analysis --- Use of --- Computers; {Fortran 77} (Computer program language)", } @InProceedings{Wong:1994:FEE, author = "W. F. Wong and E. Goto", title = "Fast evaluation of the elementary functions in double precision", crossref = "Mudge:1994:PTS", pages = "349--358", year = "1994", bibdate = "Tue Dec 12 09:29:07 MST 1995", abstract = "One of the most spectacular development in computer technology is the growth in memory density and speed. It is with this development in mind that we intend to tackle the old problem of computing the elementary functions. Since the dawn of computing, the fast and accurate computation of the elementary functions has been a constant concern of numerical computing. It now seems possible to use tables of sizes in the range of megabits to aid in such computation. To this end, in this paper, we propose a method called ATA-M (Add-Table Lookup-Add with Multiplication) for evaluating polynomials with the aid of tables. When applied to the elementary functions, we obtained a set of algorithms which computes the reciprocal, square root, exponential, sine, cosine, logarithm, are tangent and the hyperbolic functions in about 3 to 4 double precision floating point multiplication time and utilizing about 2 Mbyte of tables.", acknowledgement = ack-nhfb, affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore", bookpages = "xi + 621", classification = "C5230 (Digital arithmetic methods); C4130 (Interpolation and function approximation)", confdate = "4-7 Jan. 1994", conflocation = "Wailea, HI, USA", confsponsor = "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus. Admin", keywords = "Elementary functions; Double precision; Memory density; Memory speed; Numerical computing; ATA-M; Add-Table Lookup-Add with Multiplication; Polynomials; Hyperbolic functions; Floating point multiplication time", language = "English", pubcountry = "USA", thesaurus = "Digital arithmetic; Polynomials; Table lookup", } @Article{Wong:1994:FHB, author = "W. F. Wong and E. Goto", title = "Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers", journal = j-IEEE-TRANS-COMPUT, volume = "43", number = "3", pages = "278--294", month = mar, year = "1994", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Tue Dec 12 09:29:07 MST 1995", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", abstract = "As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be tau /sub */, our algorithms to achieve roughly 3.68 tau /sub */,4.56 tau /sub */, 5.25 tau /sub */, 3.69 tau /sub */, 7.06 tau /sub */, and 6.5 tau /sub */, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.", acknowledgement = ack-nj # " and " # ack-nhfb, affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore", classification = "C5230 (Digital arithmetic methods); C4110 (Error analysis in numerical methods)", keywords = "Hardware-based algorithms; Elementary function computations; Rectangular multipliers; Scientific computations; Common elementary functions; Reciprocal square root; Arc tangent; Sine; Cosine; Microscopic parallelism; Floating point multiplication", language = "English", pubcountry = "USA", thesaurus = "Digital arithmetic; Error analysis", } @Article{Xu:1994:VPC, author = "Guo Liang Xu and Jia Kai Li", title = "Variable precision computation of elementary functions. (Chinese)", journal = "J. Numer. Methods Comput. Appl.", volume = "15", number = "3", pages = "161--171", year = "1994", ISSN = "1000-3266", MRclass = "65D20 (65Y20)", MRnumber = "MR1357336 (96i:65013)", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, fjournal = "Journal on Numerical Methods and Computer Applications. Shuzhi Jisuan yu Jisuanji Yingyong", } @InProceedings{Chen:1995:UCA, author = "San-Gee Chen and Chieh-Chih Li", booktitle = "IEEE Signal Processing Society Workshop on VLSI Signal Processing, VIII, 1995", title = "A unified cellular array for multiplication, division and square root", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "533--541", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A unified fast, small-area processor capable of executing multiplication, division and square-root operations, all starting from MSD is proposed. Unlike the existing designs which require both addition and subtraction operations, and complicated \ldots{}", } @Article{Das:1995:IFC, author = "D. Das and K. Mukhopadhyaya and B. P. Sinha", title = "Implementation of four common functions on an {LNS} co-processor", journal = j-IEEE-TRANS-COMPUT, volume = "44", number = "1", pages = "155--161", month = jan, year = "1995", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 16:14:38 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We propose a scheme for evaluating four commonly used functions namely, (1) inverse trigonometric functions, (2) trigonometric functions, (3) the exponential function, and (4) the logarithmic function with the help of a logarithmic number system ( \ldots{}", } @Article{Daumas:1995:MRR, author = "Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller", title = "Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions", journal = j-J-UCS, volume = "1", number = "3", pages = "162--175 (electronic)", year = "1995", CODEN = "????", ISSN = "0948-6968", MRclass = "68M07 (68Q20)", MRnumber = "1 390 003", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Doman:1995:SAP, author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen", title = "A Set of {Ada} Packages for High Precision Calculations", journal = j-TOMS, volume = "21", number = "4", pages = "416--431", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 14 09:57:55 1995", acknowledgement = ack-rfb, keywords = "accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software", subject = "G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability", } @Article{Hobson:1995:EMR, author = "R. F. Hobson and M. W. Fraser", title = "An efficient maximum-redundancy radix-$8$ {SRT} division and square-root method", journal = j-IEEE-J-SOLID-STATE-CIRCUITS, volume = "30", number = "1", pages = "29--38", month = jan, year = "1995", CODEN = "IJSCBC", ISSN = "0018-9200", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.", acknowledgement = ack-nhfb, affiliation = "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada", classification = "B1265B (Logic circuits); B2570D (CMOS integrated circuits); C5230 (Digital arithmetic methods)", keywords = "Maximum-redundancy radix-8 SRT algorithm; Multiplication; Division; Square-root method; Integrated control path; Redundant partial-remainder; Parallel iterative multiplier; Partial remainder production; Maximally redundant digit set; IEEE floating point algorithm; Table lookup; CMOS adder cell; CMOS divider; 1.2 Mum", language = "English", numericalindex = "Size 1.2E-06 m", pubcountry = "USA", summary = "A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the \ldots{}", thesaurus = "Adders; CMOS digital integrated circuits; Digital arithmetic; Dividing circuits; Floating point arithmetic; Multiplying circuits", } @InProceedings{Ito:1995:EIA, author = "M. Ito and N. Takagi and S. Yajima", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995", title = "Efficient Initial Approximation and Fast Converging Methods for Division and Square Root", crossref = "Knowles:1995:PSC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "2--9", month = jul, year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-sfo # " and " # ack-nhfb, summary = "Efficient initial approximations and fast converging algorithms are important to achieve the desired precision faster at lower hardware cost in multiplicative division and square root. In this paper, a new initial approximation method for division, \ldots{}", } @InProceedings{Kwan:1995:CII, author = "H. Kwan and R. L. {Nelson, Jr.} and E. E. {Swartzlander, Jr.}", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995", title = "Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead", crossref = "Knowles:1995:PSC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "115--122", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We present an unconventional method of computing the inverse of the square root. It implements the equivalent of two iterations of a well-known multiplicative method to obtain 24-bit mantissa accuracy. We implement each ``iteration'' as a \ldots{}", } @InProceedings{Lang:1995:VHR, author = "T. Lang and P. Montuschi", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995", title = "Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding", crossref = "Knowles:1995:PSC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "124--131", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "An algorithm for square root with prescaling is developed and combined with a similar scheme for division. An implementation is described, evaluated and compared with other combined div/sqrt \ldots{}", } @Book{Lau:1995:NLC, author = "H. T. (Hang Tong) Lau", title = "A Numerical library in {C} for scientists and engineers", publisher = pub-CRC, address = pub-CRC:adr, pages = "xvii + 795", year = "1995", ISBN = "0-8493-7376-X", ISBN-13 = "978-0-8493-7376-3", LCCN = "QA76.73.C15 L38 1995", bibdate = "Fri Sep 26 14:29:10 MDT 2008", bibsource = "z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html", acknowledgement = ack-nhfb, subject = "C (Computer program language)", } @InProceedings{Leeser:1995:VSR, author = "M. Leeser and J. O'Leary", booktitle = "Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, ICCD '95", title = "Verification of a subtractive radix-$2$ square root algorithm and implementation", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "526--531", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Many modern microprocessors implement floating point square root hardware using subtractive algorithms. Such processors include the HP PA7200, the MIPS R4400, and the Intel Pentium. The Intel Pentium division bug highlights the importance of \ldots{}", } @Article{Liu:1995:SRV, author = "S.-I. Liu", title = "Square-rooting and vector summation circuits using current conveyors", journal = "IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G- Circuits, Devices and Systems]", volume = "142", number = "4", pages = "223--226", month = aug, year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "New analogue squaring, square-rooting and vector summation circuits using current conveyors (CCIIs) are presented. They consist of MOS transistors biased in the triode region, a buffered unity-gain inverting amplifier, resistors and CCIIs. A general \ldots{}", } @Article{Luther:1995:HAT, author = "Wolfram Luther", title = "Highly accurate tables for elementary functions", journal = j-BIT-NUM-MATH, volume = "35", number = "3", pages = "352--360", month = sep, year = "1995", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01732609", ISSN = "0006-3835 (print), 1572-9125 (electronic)", MRclass = "65D20 (68U05)", MRnumber = "97h:65024", bibdate = "Wed Jan 4 18:52:24 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3", URL = "http://www.mai.liu.se/BIT/contents/bit35.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352", acknowledgement = ack-nhfb, keywords = "elementary functions", } @InProceedings{Lynch:1995:KTF, author = "T. Lynch and A. Ahmed and M. Schulte and T. Callaway", title = "The {K5} Transcendental Functions", crossref = "Knowles:1995:PSC", pages = "163--171", year = "1995", bibdate = "Mon May 20 06:05:24 MDT 2002", bibsource = "OCLC Proceedings database", URL = "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf", acknowledgement = ack-nhfb, } @InProceedings{Matsubara:1995:NBS, author = "G. Matsubara and N. Ide and H. Tago and S. Suzuki and N. Goto", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995", title = "30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit", crossref = "Knowles:1995:PSC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "98--105", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A shared radix 2 division and square root implementation using a self-timed circuit is presented. The same execution time for division and square root is achieved by using an on-the-fly digit decoding and a root multiple generation technique. Most \ldots{}", } @Article{Montuschi:1995:RRI, author = "P. Montuschi and L. Ciminiera", title = "A remark on {``Reducing iteration time when result digit is zero for radix-$2$ {SRT} division and square root with redundant remainders''}", journal = j-IEEE-TRANS-COMPUT, volume = "44", number = "1", pages = "144--146", month = jan, year = "1995", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", note = "See \cite{Montuschi:1993:RIT}.", acknowledgement = ack-nhfb, summary = "In a previous paper by P. Montuschi and L. Ciminiera (ibid., vol. 42, no.2 p239-246, Feb 1993), an architecture for shared radix 2 division and square root has been presented whose main characteristic is the ability to avoid any addition/subtraction, \ldots{}", } @InProceedings{Prabhu:1995:MRD, author = "J. A. Prabhu and G. B. Zyner", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995", title = "{167 MHz} Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages", crossref = "Knowles:1995:PSC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "155--162", year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "UltraSPARC's IEEE-754 compliant floating point divide and square root implementation is presented. Three overlapping stages of SRT radix-$2$ quotient selection logic enable an effective radix-$8$ calculation at 167 MHz while only a single radix-$2$ \ldots{}", } @InProceedings{Schwarz:1995:RQC, author = "E. M. Schwarz", booktitle = "Conference Record of the Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, 1995", title = "Rounding for quadratically converging algorithms for division and square root", crossref = "Singh:1995:CRT", volume = "1", pages = "600--603", month = oct, year = "1995", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-sfo # " and " # ack-nhfb, summary = "Exactly rounded results are necessary for many architectures such as IEEE 754 standard. For division and square root, rounding is easy to perform if a remainder is available. But for quadratically converging algorithms, the remainder is not \ldots{}", } @Article{Smith:1995:CFA, author = "Roger Alan Smith", title = "A Continued-Fraction Analysis of Trigonometric Argument Reduction", journal = j-IEEE-TRANS-COMPUT, volume = "44", number = "11", pages = "1348--1351", month = nov, year = "1995", CODEN = "ITCOB4", DOI = "http://dx.doi.org/10.1109/12.475133", ISSN = "0018-9340", bibdate = "Fri Dec 08 10:21:28 2006", abstract = "The calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer $N$ and $0 \leq \alpha < 1$ such that $x = (N + \alpha) \pi/4$. This reduction modulo $\pi/4$ makes it possible to calculate a trigonometric function of a reduced argument, either $\alpha\pi/4$ or $(1 - \alpha)\pi/4$, which lies in the interval $(0, \pi/4)$. Payne and Hanek [1] described an efficient algorithm for computing $\alpha$ to a predetermined level of accuracy. They noted that if $x$ differs only slightly from an integral multiple $\pi/2$, the reduction must be carried out quite accurately to avoid loss of significance in the reduced argument. We present a simple method using continued fractions for determining, for all numbers $x$ for which the greatest number of insignificant leading bits occur. Applications are made IEEE single-precision and double-precision formats and two extended- precision formats.", acknowledgement = ack-nhfb, keywords = "argument reduction; computer arithmetic; continued fractions; nonlinear optimization; Payne/Hanek radian reduction; range reduction; trigonometric functions", } @Article{Wong:1995:EHS, author = "W. F. Wong and Yoshio Oyanagi and Eiichi Goto", title = "Evaluation of the {Hitachi S-3800} Supercomputer Using Six Benchmarks", journal = j-IJSAHPC, volume = "9", number = "1", pages = "58--70", month = "Spring", year = "1995", CODEN = "IJSAE9", ISSN = "0890-2720", bibdate = "Tue Feb 18 09:07:32 MST 1997", bibsource = "Compendex database", abstract = "The S-3000 series is the third generation of Hitachi's supercomputers. It is claimed to be currently the fastest single processor supercomputer. In this paper, we introduce the S-3000 and, using six benchmarks we designed, evaluate a member of this series of supercomputer, the top of the range S-3800, against its predecessor, the Hitachi HITAC S-820. Our purpose is to determine in what areas the S-3800 is an improvement over its predecessor. The suite of benchmarks include kernels for random number generation, elementary function computation, FFT, dense matrix operations, SOR, and list vector (scatter\slash gather) operations. The use of small-to medium-sized kernels, as opposed to large application benchmarks, help to better understand the behavior of the machine. Our findings support the claim that the S-3000 series is at least twice as fast as the previous generation of Hitachi supercomputers.", acknowledgement = ack-nhfb, affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore", affiliationaddress = "Singapore", classification = "722.4; 921.3; 921.6; 922.2", journalabr = "Int J Supercomput Appl High Perform Comput", keywords = "Benchmarks; Computer selection and evaluation; Computer testing; Fast Fourier transforms; Fastest single processor; Hitachi supercomputer; Matrix algebra; Medium sized kernels; Performance; Random number generation; Supercomputers; Vectors", } @Article{Wong:1995:FEE, author = "W. F. Wong and E. Goto", title = "Fast evaluation of the elementary functions in single precision", journal = j-IEEE-TRANS-COMPUT, volume = "44", number = "3", pages = "453--457", month = mar, year = "1995", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Dec 14 11:25:18 MST 1995", abstract = "In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.", acknowledgement = ack-nhfb, affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore", classification = "C5230 (Digital arithmetic methods); C4110 (Error analysis in numerical methods)", keywords = "Fast evaluation; Elementary functions; Single precision; Truncated Taylor series; Difference method; Adders; Reciprocal; Square root; Logarithm functions; Inverse trigonometric functions; Floating point multiplies", language = "English", pubcountry = "USA", thesaurus = "Error analysis; Floating point arithmetic", } @Article{Cappuccino:1996:DDH, author = "G. Cappuccino and P. Corsonello and G. Cocorullo", title = "Design and demonstration of high throughput square rooting circuit", journal = j-ELECT-LETTERS, volume = "32", number = "5", pages = "434", month = "", year = "1996", CODEN = "ELLEAK", ISSN = "0013-5194", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Not \ldots{}", } @InProceedings{Guyot:1996:STD, author = "A. Guyot and M. Renaudin and B. El Hassan and V. Levering", booktitle = "Proceedings of the Ninth International Conference on VLSI Design, 1996", title = "Self timed division and square-root extraction", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "376--381", year = "1996", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "This paper describes a self-timed integrated circuit for division and square-root extraction. First it concentrates on the development and the proof of a new mathematical algorithm. Then the design methodology and the architecture of a self-timed \ldots{}", } @TechReport{Hickey:1996:FSP, author = "Timothy J. Hickey and Qun Ju", title = "Fast, Sound, and Precise Narrowing of the Exponential Function", type = "Technical report", institution = "Computer Science Department, Brandeis University", address = "Waltham, MA, USA 02254", month = mar, year = "1996", bibdate = "Sat Nov 05 15:42:23 2005", URL = "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz", acknowledgement = ack-nhfb, } @Article{Lehoucq:1996:CEU, author = "R. B. Lehoucq", title = "The Computation of Elementary Unitary Matrices", journal = j-TOMS, volume = "22", number = "4", pages = "393--400", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", abstract = "The construction of elementary unitary matrices that transform a complex vector to a multiple of $e_1$, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.", accepted = "June 1996", acknowledgement = ack-rfb, keywords = "algorithms", subject = "{\bf F.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @InProceedings{Li:1996:NNR, author = "Yamin Li and Wanming Chu", booktitle = "Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96", title = "A new non-restoring square root algorithm and its {VLSI} implementations", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "538--544", year = "1996", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We present a new non-restoring square root algorithm that is very efficient to implement. The new algorithm presented here has the following features unlike other square root algorithms. First, the focus of the ``non-restoring'' is on the {\&} \ldots{}", } @TechReport{Lozier:1996:PST, author = "Daniel W. Lozier", title = "A Proposed Software Test Service for Special Functions", type = "Technical Report", number = "NISTIR 5916", institution = pub-NIST, address = pub-NIST:adr, pages = "11", month = oct, year = "1996", bibdate = "Fri Jul 09 06:02:16 2004", note = "Published in \cite{Lozier:1997:PST}.", URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps", acknowledgement = ack-nhfb, } @Article{Lozier:1996:SNS, author = "Daniel W. Lozier", title = "Software Needs in Special Functions", journal = j-J-COMP-APPL-MATH, volume = "66", number = "??", pages = "345--358", month = "????", year = "1996", CODEN = "JCAMDI", ISSN = "0377-0427", bibdate = "Fri Jul 09 05:51:55 2004", acknowledgement = ack-nhfb, remark = "See preprint \cite{Lozier:1994:SNS}.", } @Article{Macleod:1996:AMS, author = "Allan J. Macleod", title = "{Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions", journal = j-TOMS, volume = "22", number = "3", pages = "288--301", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/; http://doi.acm.org/10.1145/232826.232846", abstract = "MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @InProceedings{Rao:1996:RTS, author = "V. M. Rao and B. Nowrouzian", booktitle = "Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996", title = "Rounding techniques for signed binary arithmetic", volume = "1", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "294--297", year = "1996", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 11:25:04 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.", acknowledgement = ack-nhfb, } @Article{Schwarz:1996:HSA, author = "Eric M. Schwarz and Michael J. Flynn", title = "Hardware Starting Approximation Method and Its Application to the Square Root Operation", journal = j-IEEE-TRANS-COMPUT, volume = "45", number = "12", pages = "1356--1369", month = dec, year = "1996", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Quadratically converging algorithms for high-order arithmetic operations typically are accelerated by a starting approximation. The higher the precision of the starting approximation, the less number of iterations required for convergence. \ldots{}", } @Book{Temme:1996:SFI, author = "N. M. Temme", title = "Special functions: an introduction to the classical functions of mathematical physics", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xii + 374", year = "1996", ISBN = "0-471-11313-1", ISBN-13 = "978-0-471-11313-3", LCCN = "QC20.7.F87 T46 1996", bibdate = "Mon Nov 24 21:41:54 MST 2008", bibsource = "z3950.bibsys.no:2100/BIBSYS; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "functions, special; mathematical physics; boundary value problems", } @Article{Williams:1996:TMF, author = "K. B. Williams", title = "Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. Make sure your math library isn't the weak link in the chain", journal = j-CCCUJ, volume = "14", number = "12", pages = "49--54, 58--65", month = dec, year = "1996", CODEN = "CCUJEX", ISSN = "1075-2838", bibdate = "Thu Nov 14 06:34:33 1996", note = "Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.", acknowledgement = ack-nhfb, } @Article{Alzer:1997:SIG, author = "Horst Alzer", title = "On some inequalities for the gamma and psi functions", journal = j-MATH-COMPUT, volume = "66", number = "217", pages = "373--389", month = jan, year = "1997", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33B15 (26D07)", MRnumber = "97e:33004", MRreviewer = "Peter Schroth", bibdate = "Fri Jul 16 10:38:40 MDT 1999", bibsource = "http://www.ams.org/mcom/1997-66-217", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/", acknowledgement = ack-nhfb, } @Article{Alzer:1997:SII, author = "Horst Alzer", title = "On some inequalities for the incomplete gamma function", journal = j-MATH-COMPUT, volume = "66", number = "218", pages = "771--778", month = apr, year = "1997", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33B20 (26D07)", MRnumber = "97h:33004", bibdate = "Fri Jul 16 10:38:42 MDT 1999", bibsource = "http://www.ams.org/mcom/1997-66-218", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/", acknowledgement = ack-nhfb, } @Article{Ghanem:1997:SBF, author = "Riadh Ben Ghanem and Cl{\'e}ment Frappier", title = "Spherical {Bessel} functions and explicit quadrature formula", journal = j-MATH-COMPUT, volume = "66", number = "217", pages = "289--296", month = jan, year = "1997", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "33C10 (41A55 65D32)", MRnumber = "97c:33005", MRreviewer = "N. Hayek Calil", bibdate = "Fri Jul 16 10:38:40 MDT 1999", bibsource = "http://www.ams.org/mcom/1997-66-217", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/", acknowledgement = ack-nhfb, } @Article{Hare:1997:CPB, author = "D. E. G. Hare", title = "Computing the Principal Branch of {log-Gamma}", journal = j-J-ALG, volume = "25", number = "2", pages = "221--236", month = nov, year = "1997", CODEN = "JOALDV", DOI = "http://dx.doi.org/10.1006/jagm.1997.0881", ISSN = "0196-6774", bibdate = "Thu Mar 27 14:31:42 2008", abstract = "The log-Gamma function is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.", acknowledgement = ack-nhfb, } @InProceedings{Li:1997:PAI, author = "Yamin Li and Wanming Chu", booktitle = "Proceedings of the 1997 IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '97", title = "Parallel-array implementations of a non-restoring square root algorithm", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "690--695", year = "1997", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "In this paper we present a parallel-array implementation of a new non-restoring square root algorithm (PASQRT). The carry-save adder (CSA) is used in the parallel array. The PASQRT has several features unlike other implementations. First, it does \ldots{}", } @InCollection{Lozier:1997:PST, author = "Daniel W. Lozier", title = "A Proposed Software Test Service for Special Functions", crossref = "Boisvert:1997:QNS", pages = "167--178", year = "1997", bibdate = "Fri Jul 09 06:00:46 2004", acknowledgement = ack-nhfb, remark = "See preprint \cite{Lozier:1996:PST}.", } @TechReport{Lozier:1997:TRN, author = "Daniel W. Lozier", title = "Toward a Revised {NBS} Handbook of Mathematical Functions", type = "Technical Report", number = "NISTIR 6072", institution = pub-NIST, address = pub-NIST:adr, pages = "8", month = sep, year = "1997", bibdate = "Fri Jul 09 06:35:07 2004", URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz", acknowledgement = ack-nhfb, } @InProceedings{Matsubara:1997:LPZ, author = "G. Matsubara and N. Ide", booktitle = "Proceedings of the Third International Symposium on Advanced Research in Asynchronous Circuits and Systems, 7--10 April 1997", title = "A low power zero-overhead self-timed division and square root unit combining a single-rail static circuit with a dual-rail dynamic circuit", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "198--209", year = "1997", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "An asynchronous pipeline scheme that combines a low power static circuit with a high-speed dual-rail dynamic circuit is proposed. The scheme utilizes a dual-rail circuit only in the critical path of an SRT division and square root calculation unit. \ldots{}", } @Book{Muller:1997:EFA, author = "Jean-Michel Muller", title = "Elementary functions: algorithms and implementation", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xv + 204", year = "1997", ISBN = "0-8176-3990-X", ISBN-13 = "978-0-8176-3990-7", LCCN = "QA331.M866 1997", bibdate = "Fri Jul 25 12:00:55 1997", price = "US\$59.95", URL = "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X; http://www.ens-lyon.fr/~jmmuller/book_functions.html", acknowledgement = ack-nhfb, } @InProceedings{Schulte:1997:AFA, author = "M. J. Schulte and James E. Stine", title = "Accurate Function Approximations by Symmetric Table Lookup and Addition", crossref = "Thiele:1997:IIC", pages = "144--153", year = "1997", bibdate = "Sun Mar 04 10:55:40 2007", URL = "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf", acknowledgement = ack-nhfb, } @InProceedings{Schulte:1997:SBT, author = "M. Schulte and J. Stine", title = "Symmetric Bipartite Tables for Accurate Function Approximation", crossref = "Lang:1997:ISC", pages = "175--183", year = "1997", bibdate = "Mon May 20 05:45:32 MDT 2002", bibsource = "OCLC Proceedings database", URL = "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf", acknowledgement = ack-nhfb, } @Book{Thompson:1997:ACMa, author = "William J. (William Jackson) Thompson", title = "Atlas for computing mathematical functions: an illustrated guidebook for practitioners: with programs in {C} and {Mathematica}", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 903", year = "1997", ISBN = "0-471-00260-7 (cloth)", ISBN-13 = "978-0-471-00260-4 (cloth)", LCCN = "QA331.T385 1997", bibdate = "Fri May 21 07:11:19 MDT 1999", acknowledgement = ack-nhfb, annote = "A Wiley-Interscience publication. Includes CD-ROM.", keywords = "Functions -- Computer programs; Science -- Mathematics -- Computer programs; C (Computer program language); Mathematica (Computer program language)", } @Book{Thompson:1997:ACMb, author = "William J. (William Jackson) Thompson", title = "Atlas for computing mathematical functions: an illustrated guide for practitioners with programs in {Fortran 90} and {Mathematica}", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 888", year = "1997", ISBN = "0-471-18171-4 (cloth)", ISBN-13 = "978-0-471-18171-2 (cloth)", LCCN = "QA331.T386 1997", bibdate = "Fri May 21 07:11:19 MDT 1999", note = "Includes CD-ROM.", acknowledgement = ack-nhfb, annote = "A Wiley-Interscience publication. System requirements for accompanying computer disc: Windows; Macintosh compatible.", keywords = "Functions -- Computer programs; Science -- Mathematics -- Computer programs; FORTRAN (Computer program language); Mathematica (Computer program language)", } @Article{Aberbour:1998:PMF, author = "M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot", title = "On portable macrocell {FPU} generators for division and square root operators complying to the full {IEEE-754} standard", journal = j-IEEE-TRANS-VLSI-SYST, volume = "6", number = "1", pages = "114--121", month = mar, year = "1998", CODEN = "????", ISSN = "1063-8210", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "In this paper, we investigate the design of macrocell generators of division and square root floating-point operators. The number representation used in our operators is the IEEE-754-1985 standard for binary floating-point numbers. The design and \ldots{}", } @Article{BenGhanem:1998:QFU, author = "Riadh {Ben Ghanem}", title = "Quadrature formulae using zeros of {Bessel} functions as nodes", journal = j-MATH-COMPUT, volume = "67", number = "221", pages = "323--336", month = jan, year = "1998", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65D32", MRnumber = "98c:65031", MRreviewer = "Kai Diethelm", bibdate = "Fri Jul 16 10:38:50 MDT 1999", bibsource = "http://www.ams.org/mcom/1998-67-221", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/", acknowledgement = ack-nhfb, } @Article{Deleglise:1998:C, author = "Marc Del{\'e}glise and Jo{\"e}l Rivat", title = "Computing $\psi(x)$", journal = j-MATH-COMPUT, volume = "67", number = "224", pages = "1691--1696", month = oct, year = "1998", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "11Y35 (11N56)", MRnumber = "1 474 649", bibdate = "Fri Jul 16 10:38:58 MDT 1999", bibsource = "http://www.ams.org/mcom/1998-67-224", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/", acknowledgement = ack-nhfb, } @Article{Kiranon:1998:SRV, author = "W. Kiranon and N. Kumprasert", title = "Square-rooting and vector summation circuits using current conveyors", journal = "Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G- Circuits, Devices and Systems]", volume = "145", number = "2", pages = "139", month = apr, year = "1998", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Recently, Lui [1995] presented a square-rooting circuit using CCII, MOS transistors and a buffered unity-gain inverting amplifier. It is interesting since it finds various applications as described in his paper. However, an error occurred in the \ldots{}", } @InProceedings{Kuhlmann:1998:FLP, author = "M. Kuhlmann and K. K. Parhi", booktitle = "Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98", title = "Fast low-power shared division and square-root architecture", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "128--135", year = "1998", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "This paper addresses a fast low-power implementation of a shared division and square-root architecture. Two approaches are considered in this paper; these include the SRT (Sweeney, Robertson and Tocher) approach which does not require prescaling and \ldots{}", } @Article{Lefevre:1998:TCR, author = "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand", title = "Toward correctly rounded transcendentals", journal = j-IEEE-TRANS-COMPUT, volume = "47", number = "11", pages = "1235--1243", month = nov, year = "1998", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 11:25:04 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the \ldots{}", } @Article{Morozov:1998:NWR, author = "D. Kh. Morozov and V. V. Voitsekhovich", title = "A new wide-range approximation of modified {Bessel} functions in terms of elementary functions", journal = "Rev. Mexicana F\'\i s.", volume = "44", number = "3", pages = "231--234", year = "1998", CODEN = "RMXFAT", ISSN = "0035-001X", MRclass = "65D20", MRnumber = "MR1629601", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Revista Mexicana de F\'\i sica", } @InProceedings{Agarwal:1999:SAM, author = "R. C. Agarwal and F. G. Gustavson and M. S. Schmookler", title = "Series approximation methods for divide and square root in the {Power3{\TM}} processor", crossref = "Koren:1999:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "116--123", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", URL = "http://euler.ecs.umass.edu/paper/final/paper-144.ps; http://euler.ecs.umass.edu/paper/final/paper-144.pdf", acknowledgement = ack-nhfb, keywords = "computer arithmetic; ARITH; IEEE", summary = "The Power3 processor is a 64-bit implementation of the PowerPC TM architecture and is the successor to the Power2 TM processor for workstations and servers which REQUIRE high performance floating point capability. The previous \ldots{}", } @Article{Bach:1999:NTS, author = "E. Bach and K. Huber", title = "Note on taking square-roots modulo {N}", journal = j-IEEE-TRANS-INF-THEORY, volume = "45", number = "2", pages = "807--809", month = mar, year = "1999", CODEN = "IETTAW", ISSN = "0018-9448", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "In this article it is shown how Gauss' (1981) famous cyclotomic sum formula can be used for extracting square-roots modulo \ldots{}", } @InProceedings{Batten:1999:IBO, author = "D. Batten and S. Jinturkar and J. Glossner and M. Schulte and R. Peri and P. D'arcy", editor = "????", booktitle = "Proceedings of the International Conference on Signal Processing Applications and Technologies, Orlando, Florida, November, 1999", title = "Interactions Between Optimizations and a New Type of {DSP} Intrinsic Function", publisher = "????", address = "????", year = "1999", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sun Mar 04 11:05:23 2007", note = "Shortened version in \cite{Batten:1999:IFB}.", URL = "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf", acknowledgement = ack-nhfb, } @Article{Batten:1999:IFB, author = "D. Batten and P. D'arcy", title = "Intrinsic Functions Boost Compilers", journal = "Electrical Engineering Times", volume = "1085", pages = "104--104", month = nov, year = "1999", bibdate = "Sun Mar 04 11:06:22 2007", acknowledgement = ack-nhfb, } @InProceedings{Bui:1999:DSI, author = "H. Bui and S. Tahar", booktitle = "1999 IEEE Canadian Conference on Electrical and Computer Engineering, 9--12 May 1999", title = "Design and synthesis of an {IEEE-754} exponential function", volume = "1", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "450--455", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 17:14:11 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We have designed a floating-point exponential function using the table-driven method. The algorithm was first implemented using sequential VHDL and later translated to Concurrent Verilog. The main part of the work consisted of creating modules that \ldots{}", } @Article{Cappuccino:1999:HSS, author = "G. Cappuccino and G. Cocorullo and P. Corsonello and S. Perri", title = "High speed self-timed pipelined datapath for square rooting", journal = "Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G- Circuits, Devices and Systems]", volume = "146", number = "1", pages = "16--22", month = feb, year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The authors describe a new high-performance self-timed circuit for asynchronous square rooting. The new architecture is based on a modified nonrestoring algorithm. An asynchronous pipelined cellular array without auxiliary system for the \ldots{}", } @InProceedings{Cornea-Hasegan:1999:CPO, author = "M. A. Cornea-Hasegan and R. A. Golliver and P. Markstein", title = "Correctness proofs outline for {Newton--Raphson} based floating-point divide and square root algorithms", crossref = "Koren:1999:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "96--105", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", URL = "http://euler.ecs.umass.edu/paper/final/paper-121.ps; http://euler.ecs.umass.edu/paper/final/paper-121.pdf", acknowledgement = ack-nhfb, keywords = "computer arithmetic; ARITH; IEEE", summary = "This paper describes a study of a class of algorithms for the floating-point divide and square root operations, based on the Newton-Raphson iterative method. The two main goals were. (1) Proving the IEEE correctness of these iterative floating-point \ldots{}", } @Article{Corsonello:1999:HPS, author = "P. Corsonello and S. Perri", title = "High performance square rooting circuit using hybrid radix-$2$ adders", journal = j-ELECT-LETTERS, volume = "35", number = "3", pages = "185--186", day = "4", month = feb, year = "1999", CODEN = "ELLEAK", ISSN = "0013-5194", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A new high performance bit parallel architecture for computing square roots is proposed. The architecture implements a non-restoring algorithm and is structured as a pipelined cellular array. To improve the performance, hybrid radix-$2$ adders are \ldots{}", } @Article{Gautschi:1999:NRC, author = "Walter Gautschi", title = "A Note on the Recursive Calculation of Incomplete Gamma Functions", journal = j-TOMS, volume = "25", number = "1", pages = "101--107", month = mar, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC; http://doi.acm.org/10.1145/305658.305717", abstract = "It is known that the recurrence relation for incomplete gamma functions $\Gamma(a + n, x), 0 \le a < 1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is unstable---more so the larger $x$. Nevertheless, the recursion can be used in the range $0 \le n \le x$ practically without error growth, and in larger ranges $0 \le n \le N$ with a loss of accuracy that can be controlled by suitably limiting $N$.", acknowledgement = ack-nhfb, keywords = "algorithms; reliability", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability). {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @TechReport{Gourdon:1999:NCC, author = "Xavier Gourdon and Pascal Sebah", title = "Numbers, constants, and computation", institution = "????", address = "Paris, France", year = "1999", bibdate = "Sat Mar 15 16:28:07 2003", note = "World-Wide Web site.", URL = "http://numbers.computation.free.fr/Constants/home.html", acknowledgement = ack-nhfb, annote = "Although this site concentrates mainly on computation of particular mathematical constants, it also treats high-precision computation of inverse and square root.", } @Article{Harrison:1999:CTF, author = "John Harrison and Ted Kubaska and Shane Story and Ping Tak Peter Tang", title = "The Computation of Transcendental Functions on the {IA-64} Architecture", journal = j-INTEL-TECH-J, number = "Q4", pages = "7", day = "22", month = nov, year = "1999", bibdate = "Fri Jun 01 06:02:08 2001", URL = "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm; http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf", acknowledgement = ack-nhfb, } @InProceedings{Hyogo:1999:LVF, author = "A. Hyogo and Y. Fukutomi and K. Sekine", booktitle = "Proceedings of the 1999 IEEE International Symposium on Circuits and Systems: ISCAS '99, 2 June 1999", title = "Low voltage four-quadrant analog multiplier using square-root circuit based on {CMOS} pair", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "274--277", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We proposed a square-root circuit based on CMOS pairs. In this paper, we propose a low voltage four-quadrant analog multiplier using the square-root circuit. Also we confirmed this operation by PSpice \ldots{}", } @InProceedings{Iordache:1999:IPR, author = "C. Iordache and D. W. Matula", title = "On Infinitely Precise Rounding for Division, Square Root, Reciprocal and Square Root Reciprocal", crossref = "Koren:1999:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "233--240", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", URL = "http://euler.ecs.umass.edu/paper/final/paper-164.ps; http://euler.ecs.umass.edu/paper/final/paper-164.pdf", acknowledgement = ack-nhfb, keywords = "computer arithmetic; ARITH; IEEE", summary = "Quotients, reciprocals, square roots and square root reciprocals all have the property that infinitely precise p-bit rounded results for p-bit input operands can be obtained from approximate results of bounded accuracy. We investigate lower bounds \ldots{}", } @Article{Lang:1999:VHR, author = "T. Lang and P. Montuschi", title = "Very high radix square root with prescaling and rounding and a combined division\slash square root unit", journal = j-IEEE-TRANS-COMPUT, volume = "48", number = "8", pages = "827--841", month = aug, year = "1999", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "An algorithm for square root with prescaling and selection by rounding is developed and combined with a similar scheme for division. Since division is usually more frequent than square root, the main concern of the combined implementation is to \ldots{}", } @InProceedings{Lee:1999:STS, author = "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and Seung-Ho Hwang", booktitle = "6th International Conference on VLSI and CAD: ICVC '99", title = "Self-timed shared division and square-root implementation using full redundant signed digit numbers", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "541--544", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A radix-$2$ square root implementation for self-timed dividers using redundant signed-digit (RSD) adders is presented. In this method, two self-timed RSD adder stages are used for each result bit selection. A very efficient and simple result bit \ldots{}", } @InProceedings{Lozier:1999:DDM, author = "Daniel W. Lozier and B. R. Miller and B. V. Saunders", title = "Design of a Digital Mathematical Library for Science, Technology and Education", crossref = "IEEE:1999:PIF", pages = "118--128", year = "1999", bibdate = "Fri Jul 09 06:33:35 2004", URL = "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz", acknowledgement = ack-nhfb, remark = "Preprint: NISTIR 6297, Feb. 1999, 13 pages", } @InProceedings{Nannarelli:1999:LPR, author = "A. Nannarelli and T. Lang", booktitle = "(ICCD '99) International Conference on Computer Design", title = "Low-power radix-$4$ combined division and square root", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "236--242", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Because of the similarities in the algorithm it is quite common to implement division and square root in the same unit. The purpose of this work is to implement a low-power combined radix-$4$ division and square root floating-point double precision \ldots{}", } @InProceedings{Oberman:1999:FPD, author = "S. F. Oberman", title = "Floating point division and square root algorithms and implementation in the {AMD-K7{\TM}} microprocessor", crossref = "Koren:1999:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "106--115", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", URL = "http://euler.ecs.umass.edu/paper/final/paper-139.ps; http://euler.ecs.umass.edu/paper/final/paper-139.pdf", acknowledgement = ack-nhfb, keywords = "computer arithmetic; ARITH; IEEE", summary = "This paper presents the AMD-K7 IEEE 754 and $\times$87 compliant floating point division and square root algorithms and implementation. The AMD-K7 processor employs an iterative implementation of a series expansion to converge quadratically to the \ldots{}", } @InProceedings{Parhami:1999:ALT, author = "B. Parhami", booktitle = "Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers, 1999", title = "Analysis of the lookup table size for square-rooting", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1327--1330", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Convergence methods are widely used for division, reciprocation, and square-rooting. With such methods, it is common to use an initial table lookup step for obtaining an approximate result that leads to faster convergence. In the case of division \ldots{}", } @Article{Schraudolph:1999:FCA, author = "N. N. Schraudolph", title = "A Fast, Compact Approximation of the Exponential Function", journal = j-NEURAL-COMP, volume = "11", number = "4", publisher = "MIT Press", pages = "853--862", day = "1", month = may, year = "1999", CODEN = "NEUCEB", ISSN = "0899-7667", bibdate = "Fri Nov 8 05:39:32 MST 2002", bibsource = "Ingenta database", acknowledgement = ack-nhfb, pagecount = "10", } @Article{Schulte:1999:AEF, author = "M. Schulte and J. Stine", title = "Approximating Elementary Functions with Symmetric Bipartite Tables", journal = j-IEEE-TRANS-COMPUT, volume = "48", number = "8", pages = "842--847", year = "1999", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Fri Jun 24 20:20:58 2005", URL = "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf", acknowledgement = ack-nhfb, } @InProceedings{Schulte:1999:ESO, author = "M. J. Schulte and K. E. Wires", title = "Efficient Second Order Approximations for Reciprocals and Square Roots", crossref = "Luk:1999:PSA", volume = "3807", pages = "10--18", year = "1999", bibdate = "Sun Mar 04 11:10:48 2007", URL = "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf", acknowledgement = ack-nhfb, } @InProceedings{Schulte:1999:HSI, author = "Michael J. Schulte and Kent E. Wires", title = "High-Speed Inverse Square Roots", crossref = "Koren:1999:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "124--131", year = "1999", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", URL = "http://euler.ecs.umass.edu/paper/final/paper-109.ps; http://euler.ecs.umass.edu/paper/final/paper-109.pdf", acknowledgement = ack-nhfb, keywords = "computer arithmetic; ARITH; IEEE", summary = "Inverse square roots are used in several digital signal processing, multimedia, and scientific computing applications. This paper presents a high-speed method for computing inverse square roots. This method uses a table lookup, operand modification, \ldots{}", } @Article{Seidel:1999:HSR, author = "P.-M. Seidel", title = "High-speed redundant reciprocal approximation", journal = j-INTEGRATION-VLSI-J, volume = "28", number = "1", publisher = "Elsevier Science", pages = "1--12", month = sep, year = "1999", CODEN = "IVJODL", ISSN = "0167-9260", bibdate = "Fri Nov 8 05:39:32 MST 2002", bibsource = "Ingenta database", acknowledgement = ack-nhfb, pagecount = "12", } @Article{Stine:1999:STA, author = "E. Stine and M. J. Schulte", title = "The Symmetric Table Addition Method for Accurate Function Approximation", journal = j-J-VLSI-SIGNAL-PROC, volume = "21", number = "2", pages = "167--177", month = jun, year = "1999", CODEN = "JVSPED", ISSN = "0922-5773", bibdate = "Sun Mar 04 11:02:59 2007", URL = "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf", acknowledgement = ack-nhfb, } @InProceedings{Story:1999:NAI, author = "S. Story and P. T. P. Tang", title = "New Algorithms for Improved Transcendental Functions on {IA-64}", crossref = "Koren:1999:ISC", pages = "4--11", year = "1999", bibdate = "Mon Feb 7 07:28:26 MST 2000", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://euler.ecs.umass.edu/paper/final/paper-118.pdf; http://euler.ecs.umass.edu/paper/final/paper-118.ps", acknowledgement = ack-nhfb, keywords = "ARITH; computer arithmetic; IEEE", } @Article{Wieder:1999:ANH, author = "Thomas Wieder", title = "{Algorithm 794}: Numerical {Hankel} transform by the {Fortran} program {HANKEL}", journal = j-TOMS, volume = "25", number = "2", pages = "240--250", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/317275.317284; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH; http://www.netlib.org/toms/794; ftp://netlib.bell-labs.com/netlib/toms/794.gz; http://www.netlib.no/netlib/toms/794; http://www.hensa.ac.uk/netlib/toms/794.gz; http://phase.etl.go.jp/netlib/toms/794", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", abstract = "The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.", accepted = "February 1999", acknowledgement = ack-nhfb, keywords = "Hankel transform; numerical analysis", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computation of transforms;", } @Article{Alhargan:2000:ACA, author = "Fayez A. Alhargan", title = "Algorithms for the Computation of all {Mathieu} Functions of Integer Orders", journal = j-TOMS, volume = "26", number = "3", pages = "390--407", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/358407.358420", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$).", accepted = "19 May 2000", acknowledgement = ack-nhfb, } @Article{Alhargan:2000:ASC, author = "Fayez A. Alhargan", title = "{Algorithm 804}: subroutines for the computation of {Mathieu} functions of integer orders", journal = j-TOMS, volume = "26", number = "3", pages = "408--414", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/358407.358422", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.", accepted = "19 May 2000", acknowledgement = ack-nhfb, } @Article{Anderson:2000:RAF, author = "Stuart Anderson", title = "Remark on {Algorithm 723}: {Fresnel} integrals", journal = j-TOMS, volume = "26", number = "4", pages = "617--617", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/365723.365737", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", accepted = "16 October 2000", acknowledgement = ack-nhfb, } @InProceedings{Batten:2000:NAD, author = "D. Batten and S. Jinturkar and J. Glossner and M. Schulte and P. D'arcy", title = "A New Approach to {DSP} Intrinsic Functions", crossref = "Sprague:2000:PAH", pages = "2892--2901", year = "2000", bibdate = "Sun Mar 04 11:18:38 2007", URL = "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf", acknowledgement = ack-nhfb, } @Book{Bressoud:2000:CCN, author = "David M. Bressoud and S. Wagon", title = "A course in computational number theory", publisher = "Key College Publishers in cooperation with Springer", address = "New York, NY, USA", pages = "xii + 367", year = "2000", ISBN = "1-93019-010-7", ISBN-13 = "978-1-93019-010-8", LCCN = "QA241 .B788 2000", bibdate = "Fri Sep 26 14:29:31 MDT 2008", bibsource = "z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html; http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html", acknowledgement = ack-nhfb, subject = "Number theory; Algorithms", } @Article{Cawley:2000:FCA, author = "G. C. Cawley", title = "On a Fast, Compact Approximation of the Exponential Function", journal = j-NEURAL-COMP, volume = "12", number = "9", publisher = "MIT Press", pages = "2009--2012", day = "1", month = sep, year = "2000", CODEN = "NEUCEB", ISSN = "0899-7667", bibdate = "Fri Nov 8 05:39:32 MST 2002", bibsource = "Ingenta database", acknowledgement = ack-nhfb, pagecount = "4", } @Article{Cherri:2000:PCC, author = "A. K. Cherri and M. S. Alam", title = "Parallel computation of complex elementary functions using quaternary signed-digit arithmetic", journal = "Optics and Laser Technology", volume = "32", number = "6", publisher = "Elsevier Science", pages = "391--399", year = "2000", CODEN = "????", ISSN = "0030-3992", bibdate = "Sat Dec 7 09:21:28 MST 2002", bibsource = "Ingenta database", acknowledgement = ack-nhfb, pagecount = "9", } @InProceedings{Chu:2000:CPT, author = "Wanming Chu and Yamin Li", booktitle = "ACAC 2000: 5th Australasian Computer Architecture Conference", title = "Cost\slash performance tradeoff of $n$-select square root implementations", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "9--16", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Hardware square-root units require large numbers of gates even for iterative implementations. In this paper we present four low-cost high-performance fully-pipelined n-select implementations (nS-Root) based on a non-restoring-remainder square root \ldots{}", } @Article{Ercegovac:2000:IGD, author = "Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei", title = "Improving {Goldschmidt} Division, Square Root, and Square Root Reciprocal", journal = j-IEEE-TRANS-COMPUT, volume = "49", number = "7", pages = "759--763", month = jul, year = "2000", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/; OCLC Proceedings database", acknowledgement = ack-nhfb, remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.", summary = "The aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term \ldots{}", } @Article{Ercegovac:2000:RSR, author = "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel Muller and Arnaud Tisserand", title = "Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers", journal = j-IEEE-TRANS-COMPUT, volume = "49", number = "7", pages = "628--637", month = jul, year = "2000", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "68M07 (65B15)", MRnumber = "MR1783602 (2001e:68016)", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/; OCLC Proceedings database", acknowledgement = ack-nhfb, fjournal = "Institute of Electrical and Electronics Engineers. Transactions on Computers", remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.", summary = "This paper deals with the computation of reciprocals, square roots, inverse square roots, and some elementary functions using small tables, small multipliers, and, for some functions, a final ``large'' (almost full-length) multiplication. \ldots{}", } @Article{Favati:2000:SAC, author = "P. Favati and G. Lotti and O. Menchi and F. Romani", title = "Separable asymptotic cost of evaluating elementary functions", journal = j-NUMER-ALGORITHMS, volume = "24", number = "3", publisher = "Kluwer Academic Publishers, Dordrecht, The Netherlands", pages = "255--274", year = "2000", CODEN = "NUALEG", ISSN = "1017-1398", MRclass = "65Y20", MRnumber = "MR1780414 (2001d:65174)", bibdate = "Wed Apr 13 06:46:35 2005", bibsource = "Ingenta database", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", pagecount = "20", } @InProceedings{Hasan:2000:FPI, author = "M. A. Hasan and A. A. Hasan and S. Rahman", booktitle = "Proceedings of the 39th IEEE Conference on Decision and Control", title = "Fixed point iterations for computing square roots and the matrix sign function of complex matrices", volume = "5", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "4253--4258", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The purpose of this work has been the development of new set of rational iterations for computing square roots and the matrix sign function of complex matrices. Given any positive integer r{\&}ges;2, we presented a systematic way of deriving rth order \ldots{}", } @InProceedings{Hassibi:2000:ESR, author = "B. Hassibi", booktitle = "Proceedings. 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '00, 5--9 June 2000", title = "An efficient square-root algorithm for {BLAST}", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "II737--II740", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for transmitting information over a rich-scattering wireless environment using multiple receive and transmit antennas. The main computational bottleneck in the BLAST algorithm is a ``nulling and \ldots{}", } @InProceedings{Hassibi:2000:FSR, author = "B. Hassibi", booktitle = "Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000.", title = "A fast square-root implementation for {BLAST}", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1255--1259", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for transmitting information over a rich-scattering wireless environment using multiple receive and transmit antennas. The main computational bottleneck in the BLAST algorithm is a ``nulling and \ldots{}", } @InProceedings{Lefevre:2000:CRF, author = "V. D. Lefevre and J.-M. Muller", booktitle = "Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000", title = "Correctly rounded functions for better arithmetic", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "875--878", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 11:25:05 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The IEEE 754 standard for floating-point arithmetic requires that the four arithmetic operations and the square root should be correctly rounded. This has improved the accuracy, reliability and portability of numerical software. Unfortunately, such \ldots{}", } @InProceedings{Lozier:2000:DPN, author = "Daniel W. Lozier", title = "The {DLMF Project}: {A} New Initiative in Classical Special Functions", crossref = "Dunkl:2000:PIW", pages = "207--220", year = "2000", bibdate = "Fri Jul 09 06:31:32 2004", acknowledgement = ack-nhfb, } @Book{Markstein:2000:IEF, author = "Peter Markstein", title = "{IA-64} and elementary functions: speed and precision", publisher = pub-PH, address = pub-PH:adr, pages = "xix + 298", year = "2000", ISBN = "0-13-018348-2", ISBN-13 = "978-0-13-018348-4", LCCN = "QA76.9.A73 M365 2000", bibdate = "Fri Jan 5 08:00:52 MST 2001", bibsource = "University of California MELVYL catalog.", series = "Hewlett-Packard professional books", acknowledgement = ack-nhfb, annote = "Besides recipes for accurate computation of elementary functions, this book also contains algorithms for the correctly-rounded computation of floating-point division and square-root, and of integer division, starting from low-precision reciprocal approximations. There is also a wealth of information on the tradeoffs between integer and floating-point instruction use in a pipelined parallel architecture.", keywords = "IA-64 (computer architecture)", } @Article{Paliouras:2000:FPP, author = "V. Paliouras and K. Karagianni and T. Stouraitis", title = "A floating-point processor for fast and accurate sine\slash cosine evaluation", journal = j-IEEE-TRANS-CIRCUITS-SYST-2, volume = "47", number = "5", pages = "441--451", month = may, year = "2000", CODEN = "ICSPE5", ISSN = "1057-7130", bibdate = "Sat Jul 16 08:40:52 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A VLSI architecture for fast and accurate floating-point sine/cosine evaluation is presented, combining floating-point and simple fixed-point arithmetic. The algorithm implemented by the architecture is based on second order polynomial interpolation \ldots{}", } @InProceedings{Takahashi:2000:IMP, author = "D. Takahashi", booktitle = "Proceedings of the 2000 International Workshops on Parallel Processing", title = "Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "229--235", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We present efficient parallel algorithms for multiple-precision division and square root operation of more than several million decimal digits on distributed-memory parallel computers. It is well known that multiple-precision division and square \ldots{}", } @InProceedings{Tchoumatchenko:2000:FBS, author = "V. Tchoumatchenko and T. Vassileva and P. Gurov", booktitle = "Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'.", title = "A {FPGA} based square-root coprocessor", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "520--525", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We present an FPGA implementation of a non-restoring integer square-root algorithm, that uses estimates for result-digit selection and radix-$2$ redundant addition in recurrence. On-the-fly conversion of the result-digit and signed-digit adder/ \ldots{}", } @InProceedings{Tommiska:2000:AEI, author = "M. T. Tommiska", booktitle = "Proceedings of the 2000 Third IEEE International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000", title = "Area-efficient implementation of a fast square root algorithm", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "S18/1--S18/4", year = "2000", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "An area-efficient implementation of a fast-converging square-root algorithm is presented. The design of special arithmetic operations differs in many ways from the traditional tasks that digital designers are used to, and the role of \ldots{}", } @Article{Bashagha:2001:NRS, author = "A. E. Bashagha", title = "Novel radix-$2$ $k$ square root module", journal = "Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G- Circuits, Devices and Systems]", volume = "148", number = "4", pages = "190--196", month = aug, year = "2001", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The conventional two's complement radix-$2$ k square root algorithm requires a set of 2 k full precision comparisons to generate all the 2 k possible values of the partial remainder. The correct remainder is the minimum \ldots{}", } @Article{Berry:2001:WSF, author = "Michael Berry", title = "Why are special functions special?", journal = j-PHYS-TODAY, volume = "54", number = "4", pages = "11--12", year = "2001", CODEN = "PHTOAD", ISSN = "0031-9228", bibdate = "Sat Feb 19 13:23:33 2005", acknowledgement = ack-nhfb, } @Article{Boisvert:2001:MM, author = "Ronald F. Boisvert and M. J. Donahue and Daniel W. Lozier and R. McMichael and B. W. Rust", title = "Mathematics and Measurement", journal = "NIST Journal of Research", volume = "106", number = "1", pages = "293--313", month = jan # "\slash " # feb, year = "2001", bibdate = "Fri Jul 09 06:26:11 2004", acknowledgement = ack-nhfb, } @InProceedings{Burgess:2001:DIR, author = "N. Burgess and C. Hinds", booktitle = "Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001", title = "Design issues in radix-$4$ {SRT} square root {\&} divide unit", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1646--1650", year = "2001", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "This paper introduces a number of design issues not covered in the open literature that arose during the design of a radix-$4$ SRT divide/square root unit for a vector processing chip. These include compression of the partial remainder's m.s.b.'s, \ldots{}", } @InCollection{Corless:2001:RAE, author = "Robert M. Corless and James H. Davenport and David J. Jeffrey and Gurjeet Litt and Stephen M. Watt", booktitle = "Artificial intelligence and symbolic computation (Madrid, 2000)", title = "Reasoning about the elementary functions of complex analysis", volume = "1930", publisher = pub-SV, address = pub-SV:adr, pages = "115--126", year = "2001", MRclass = "68W30 (30C35)", MRnumber = "MR1882755 (2002m:68126)", bibdate = "Wed Apr 13 06:46:35 2005", series = "Lecture Notes in Comput. Sci.", acknowledgement = ack-nhfb, } @Article{Eklund:2001:CEF, author = "Neil Eklund", title = "{CORDIC}: elementary function computation using recursive sequences", journal = "College Math. J.", volume = "32", number = "5", pages = "330--333", year = "2001", ISSN = "0746-8342", MRclass = "65D20", MRnumber = "MR1868594", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "The College Mathematics Journal", } @Unpublished{Godfrey:2001:NCC, author = "P. Godfrey", title = "A Note on the Computation of the Convergent Lanczos Complex Gamma Approximation", year = "2001", bibdate = "Mon Nov 24 21:04:40 2008", note = "Unpublished Web file.", URL = "http://my.fit.edu/?gabdo/gamma.txt", acknowledgement = ack-nhfb, } @InProceedings{Lang:2001:CRR, author = "Tom{\'a}s Lang and Elisardo Antelo", booktitle = "Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001", title = "Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation", crossref = "Burgess:2001:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "83--93", year = "2001", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We present a reciprocal square-root algorithm by digit recurrence and selection by a staircase function, and the radix-$4$ implementation. As similar algorithms for division and square-root, the results are obtained correctly rounded in a \ldots{}", } @TechReport{Li:2001:LLF, author = "Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas", title = "The {\tt libm} library and floating-point arithmetic for {HP-UX} on {Itanium}", type = "Technical report", institution = "Hewlett-Packard Company", address = "Palo Alto, CA, USA", pages = "??", month = apr, year = "2001", bibdate = "Fri Jun 24 20:12:09 2005", URL = "http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html; http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf", acknowledgement = ack-nhfb, } @Article{Loenko:2001:CEF, author = "M. Yu. Loenko", title = "Computation of elementary functions with guaranteed accuracy", journal = j-PROGRAMMIROVANIE, volume = "2", pages = "68--80", year = "2001", CODEN = "PROGD3", ISSN = "0132-3474", MRclass = "65D15 (65G20)", MRnumber = "MR1867584", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Rossi\u\i skaya Akademiya Nauk. Programmirovanie", } @Article{Rump:2001:RPS, author = "Siegfried M. Rump", title = "Rigorous and Portable Standard Functions", journal = j-BIT-NUM-MATH, volume = "41", number = "3", pages = "540--562", month = jun, year = "2001", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1023/A:1021971313412", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 15:06:04 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540", abstract = "Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.", acknowledgement = ack-nhfb, keywords = "elementary functions; floating-point arithmetic", } @Article{Smith:2001:AFS, author = "David M. Smith", title = "{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions", journal = j-TOMS, volume = "27", number = "4", pages = "377--387", month = dec, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", acknowledgement = ack-nhfb, } @InProceedings{Takagi:2001:HAC, author = "N. Takagi", booktitle = "Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001", title = "A Hardware Algorithm for Computing Reciprocal Square Root", crossref = "Burgess:2001:ISC", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "94--100", year = "2001", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "OCLC Proceedings database; http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A hardware algorithm for computing the reciprocal square root which appears frequently in multimedia and graphics applications is proposed. The reciprocal square root is computed by iteration of carry-propagation-free additions, shifts, and \ldots{}", } @InProceedings{Zheng:2001:ARE, author = "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui", booktitle = "Proceedings of the 4th International Conference on ASIC", title = "The application of redundant encoding in iterative implementation of division and square root", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "603--606", year = "2001", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "The purpose of this paper is to discuss the speed improvement in division and square root computation with small area penalty. The digit recurrence SRT algorithm and functional iteration Newton-Raphson algorithm are generally used in modern \ldots{}", } @Misc{Ziv:2001:APM, author = "Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman", title = "Accurate Portable Mathematical Library ({IBM APMathLib})", howpublished = "World-Wide Web document", publisher = pub-IBM, address = pub-IBM:adr, day = "20", month = dec, year = "2001", bibdate = "Wed Nov 24 08:06:54 2004", URL = "http://oss.software.ibm.com/mathlib/; ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz", acknowledgement = ack-nhfb, } @InCollection{Boisvert:2002:HMF, author = "Ronald F. Boisvert and Daniel W. Lozier", title = "Handbook of Mathematical Functions", crossref = "Lide:2002:CEM", pages = "135--139", year = "2002", bibdate = "Fri Jul 09 06:28:13 2004", note = "Also printed as NIST Special Publication 958, Jan. 2001.", acknowledgement = ack-nhfb, } @Article{Bradford:2002:RAE, author = "Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt", title = "Reasoning about the elementary functions of complex analysis", journal = j-ANN-MATH-ARTIF-INTELL, volume = "36", number = "3", pages = "303--318", year = "2002", CODEN = "AMAIEC", ISSN = "1012-2443", MRclass = "30-01 (03B35 68W30)", MRnumber = "MR1950025 (2003m:30001)", bibdate = "Wed Apr 13 06:46:35 2005", note = "Artificial intelligence and symbolic computation (Madrid, 2000)", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematics and Artificial Intelligence", } @InProceedings{Bradford:2002:TBS, author = "Russell Bradford and James H. Davenport", booktitle = "Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation", title = "Towards better simplification of elementary functions", publisher = pub-ACM, address = pub-ACM:adr, pages = "16--22 (electronic)", year = "2002", MRclass = "68W30 (33B10)", MRnumber = "MR2035228", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, } @Article{Gil:2002:AAB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77} routines for the computation of complex {Airy} functions", journal = j-TOMS, volume = "28", number = "3", pages = "325--336", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/569147.569150", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $Ai(z)$, $Bi(z)$ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.", acknowledgement = ack-nhfb, } @Article{McCluskey:2002:MLF, author = "Glen McCluskey", title = "Math Library Functions in {C9X}", journal = j-LOGIN, volume = "27", number = "2", pages = "8--13", month = apr, year = "2002", CODEN = "LOGNEM", ISSN = "1044-6397", bibdate = "Tue Apr 11 10:52:14 MDT 2006", bibsource = "http://www.usenix.org/publications/login/2002-04/index.html", URL = "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf", acknowledgement = ack-nhfb, remark = "This is a short tutorial on some of the new math library functions in C99.", } @InProceedings{Pineiro:2002:HRL, author = "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera", booktitle = "Application-Specific Systems, Architectures and Processors, 2002. Proceedings. The IEEE International Conference on. 17--19 July 2002", title = "High-radix logarithm with selection by rounding", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "101--110", year = "2002", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 11:25:05 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A high-radix digit-recurrence algorithm or the computation of the logarithm is presented in this paper. Selection by rounding is used in iterations j/spl ges/2, and selection by table in the first iteration is combined with a restricted digit-set \ldots{}", } @Article{Pineiro:2002:HSD, author = "J. A. Pi{\~n}eiro and J. D. Bruguera", title = "High-Speed Double Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root", journal = j-IEEE-TRANS-COMPUT, volume = "51", number = "12", pages = "1377--1388", month = dec, year = "2002", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to \ldots{}", } @InProceedings{Beaumont:2003:BSE, author = "James Beaumont and Russell Bradford and James H. Davenport", booktitle = "Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation", title = "Better simplification of elementary functions through power series", publisher = pub-ACM, address = pub-ACM:adr, pages = "30--36 (electronic)", year = "2003", MRclass = "33F10 (68W30)", MRnumber = "MR2035192 (2005e:33018)", MRreviewer = "Ekatherina A. Karatsuba", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, remark = "A new algorithm testing the correctness of simplifications of elementary functions in the presence of branch cuts is proposed.", } @Article{Dominici:2003:NDS, author = "Diego Dominici", title = "Nested derivatives: a simple method for computing series expansions of inverse functions", journal = j-INT-J-MATH-MATH-SCI, volume = "58", pages = "3699--3715", year = "2003", ISSN = "0161-1712", CODEN = "????", MRclass = "41A58 (33F10)", MRnumber = "MR2031140 (2005f:41079)", MRreviewer = "Tord H. Ganelius", URL = "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf", abstract = "We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses of some special functions.", keywords = "Maple; error function, erf(x); incomplete gamma function, gamma(nu,x); sine integral, Si(x); logarithm integral, li(x); incomplete beta function, B(nu,mu,x)", } @InProceedings{Ercegovac:2003:DRA, author = "M. D. Ercegovac and J.-M. Muller", booktitle = "Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2003", title = "Digit-recurrence algorithms for division and square root with limited precision primitives", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1440--1444", year = "2003", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We propose a digit-recurrence algorithm for square root using limited-precision multipliers, adders, and table-lookups. The algorithm, except in the initialization, uses the digit-recurrence algorithm for division with limited-precision primitives \ldots{}", } @Article{Fabijonas:2003:ACM, author = "B. R. Fabijonas and Daniel W. Lozier and J. M. Rappoport", title = "Algorithms and Codes for the {Macdonald} Function: Recent Progress and Comparisons", journal = j-J-COMP-APPL-MATH, volume = "161", number = "1", pages = "179--192", month = "????", year = "2003", CODEN = "JCAMDI", ISSN = "0377-0427", MRclass = "33F05 (33C10 65D20)", MRnumber = "MR2018582", bibdate = "Fri Jul 09 06:21:51 2004", URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps", acknowledgement = ack-nhfb, } @Article{Gil:2003:CSF, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing Special Functions by Using Quadrature Rules", journal = j-NUMER-ALGORITHMS, volume = "33", number = "1--4", pages = "265--275", month = aug, year = "2003", CODEN = "NUALEG", ISSN = "1017-1398", bibdate = "Mon Sep 29 08:37:11 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf", acknowledgement = ack-nhfb, } @Article{Lang:2003:RRS, author = "Tom{\'a}s Lang and Elisardo Antelo", title = "Radix-$4$ Reciprocal Square-root and Its Combination with Division and Square Root", journal = j-IEEE-TRANS-COMPUT, volume = "52", number = "9", pages = "1100--1114", month = sep, year = "2003", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, abstract = "In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-$4$ implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for $j \geq 2$ (the selection constants are different for $j = 0$, $j = 1$, and $j \geq 2$), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.", } @TechReport{Lefevre:2003:WCC, author = "Vincent Lef{\`e}vre and Jean-Michel Muller", title = "Worst Cases for Correct Rounding for the Elementary Functions in Double Precision", type = "Technical report", institution = "INRIA, Projet Spaces, LORIA, Campus Scientifique", address = "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex, France", day = "14", month = aug, year = "2003", bibdate = "Thu Jul 08 08:27:53 2004", URL = "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf", abstract = "We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.", acknowledgement = ack-nhfb, keywords = "elementary functions; floating-point arithmetic; computer arithmetic; Table Maker's Dilemma", } @Article{Lozier:2003:NDL, author = "Daniel W. Lozier", title = "{NIST Digital Library of Mathematical Functions}", journal = j-ANN-MATH-ARTIF-INTELL, volume = "38", number = "1--3", pages = "105--119", month = may, year = "2003", CODEN = "AMAIEC", ISSN = "1012-2443", bibdate = "Fri Jul 09 06:23:08 2004", URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps", acknowledgement = ack-nhfb, } @InProceedings{Markstein:2003:FQP, author = "Peter Markstein", title = "A fast quad precision elementary function library for {Itanium}", crossref = "Anonymous:2003:CRN", pages = "5--12", year = "2003", bibdate = "Fri Jun 24 20:14:39 2005", abstract = "This talk will describe Itanium's floating point architecture and how it has been used to produce a high performance, highly accurate quad precision elementary function library.\par Itanium's floating-point features will first be described, from the point of view of a computer architect. Many conflicting requirements vie for consideration during the design of a new computer architecture. These include instruction word size, number of registers, the set of operations, arithmetic precisions supported, and memory access. Some of the trade-offs during the design phase will be discussed.\par One of the objectives of the original Itanium design was to accelerate quad precision arithmetic. The talk will describe how the Itanium elementary function library was constructed, with attention to performance and accuracy. Because a pair of double-extended floating point words are used for internal operations involving quad precision numbers, intermediate results, holding 128 bits, provide 15 guard bits during intermediate calculations, resulting in a very low percentage of misrounded results.", acknowledgement = ack-nhfb, } @InProceedings{Pineiro:2003:LHR, author = "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac", booktitle = "2003. ISCAS '03. Proceedings of the 2003 International Symposium on Circuits and Systems. 25--28 May 2003", title = "On-line high-radix exponential with selection by rounding", volume = "4", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "IV-121--IV-124", year = "2003", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 11:25:05 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "An on-line high-radix algorithm for computing the exponential function (e/sup x/) with arbitrary precision n is presented. Selection by rounding and a redundant digit-set for the digits e/sub j/ are used, with selection by table in the first \ldots{}", } @InProceedings{Wang:2003:TDF, author = "Xiaojun Wang and B. E. Nelson", booktitle = "FCCM 2003: 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 9--11 April 2003", title = "Tradeoffs of designing floating-point division and square root on {Virtex FPGAs}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "195--203", year = "2003", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "Low latency, high throughput and small area are three major design considerations of an FPGA (field programmable gate array) design. In this paper, we present a high radix SRT division algorithm and a binary restoring square root algorithm. We \ldots{}", } @Article{Berrut:2004:APS, author = "Jean-Paul Berrut and Hans D. Mittelmann", title = "Adaptive Point Shifts in Rational Approximation with Optimized Denominator", journal = j-J-COMP-APPL-MATH, volume = "164--165", number = "??", pages = "81--92", day = "1", month = mar, year = "2004", CODEN = "JCAMDI", DOI = "http://dx.doi.org/10.1016/S0377-0427(03)00485-0", ISSN = "0377-0427", bibdate = "Tue Mar 24 21:10:48 2009", note = "Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M.J. Goovaerts, S. Vandewalle, and L. Wuytack.", abstract = "Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.", acknowledgement = ack-nhfb, keywords = "rational approximation; interpolation; optimal interpolation; point shifts", } @Article{Brisebarre:2004:ACR, author = "N. Brisebarre and J.-M. Muller and Saurabh Kumar Raina", title = "Accelerating correctly rounded floating-point division when the divisor is known in advance", journal = j-IEEE-TRANS-COMPUT, volume = "53", number = "8", pages = "1069--1072", month = aug, year = "2004", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Sat Jul 16 08:40:52 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "We present techniques for accelerating the floating-point computation of $x/y$ when $y$ is known before $x$. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with \ldots{}", acknowledgement = ack-nhfb, summary = "We present techniques for accelerating the floating-point computation of x/y when y is known before x. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with \ldots{}", } @Article{Defour:2004:PSM, author = "David Defour and Guillaume Hanrot and Vincent Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol and Paul Zimmermann", title = "Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic", journal = j-NUMER-ALGORITHMS, volume = "37", number = "1--4", pages = "367--375", month = dec, year = "2004", CODEN = "NUALEG", ISSN = "1017-1398", bibdate = "Mon Dec 6 07:00:28 MST 2004", bibsource = "http://www.kluweronline.com/issn/1017-1398", URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm; http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf; http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf", acknowledgement = ack-nhfb, remark = "Special Issue: SCAN'2002 International Conference (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)", } @InProceedings{Doss:2004:FBI, author = "C. C. Doss and R. L. {Riley, Jr.}", booktitle = "FCCM 2004. 12th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 20--23 April 2004", title = "{FPGA}-based implementation of a robust {IEEE-754} exponential unit", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "229--238", year = "2004", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 17:14:11 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "This work explores the feasibility of implementing a floating-point exponentiation unit on reconfigurable computing systems. A table-driven exponentiation unit was implemented using synthesizable VHDL. The project included creating pipelined \ldots{}", } @InProceedings{Ercegovac:2004:CSRb, author = "M. D. Ercegovac and J.-M. Muller", booktitle = "Proceedings of the 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004", title = "Complex square root with operand prescaling", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "52--62", year = "2004", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "We propose a radix-r digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation. Moreover, the use of digit \ldots{}", } @Article{Fabijonas:2004:AAF, author = "B. R. Fabijonas", title = "{Algorithm 838}: {Airy} Functions", journal = j-TOMS, volume = "30", number = "4", pages = "491--501", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1039813.1039819", ISSN = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.", acknowledgement = ack-nhfb, } @Article{Fabijonas:2004:CCA, author = "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver", title = "Computation of complex {Airy} functions and their zeros using asymptotics and the differential equation", journal = j-TOMS, volume = "30", number = "4", pages = "471--490", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1039813.1039818", ISSN = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.", acknowledgement = ack-nhfb, } @InProceedings{Gebali:2004:EAF, author = "Fayez Gebali and Mohamed Watheq El-Kharashi", title = "{ERL}: an algorithm for fast evaluation of exponential, reciprocal, and logarithmic functions", crossref = "Wahdan:2004:IHE", pages = "269--272", year = "2004", bibdate = "Sat Jul 16 18:04:58 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "A fast algorithm (ERL) is proposed for evaluating Exponential, Reciprocal, and Logarithmic functions. The algorithm requires two to three iterations to complete using simple operations such as multiply, accumulate, and table lookup. The algorithm is independent of the number format used by the machine. Thus it can be implemented using the IEEE 754 floating-point standard or any other special format used by special-purpose processors. The dynamic range of the algorithm is limited only by the dynamic range of the machine on which it is implemented Numerical simulations are performed which verifies the speed and accuracy of the algorithm.", acknowledgement = ack-nhfb, } @Article{Gil:2004:AMB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 831}: {Modified} {Bessel} functions of imaginary order and positive argument", journal = j-TOMS, volume = "30", number = "2", pages = "159--164", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/992200.992204", ISSN = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $x^2 w'' + xw' + (a^2 - x^2)w = 0$. The code also computes exponentially scaled functions. The range of computation is $(x, a) \in (0,1500] \times [-1500, 1500]$ when scaled functions are considered and it is larger than $(0,500] \times [-400, 400]$ for standard IEEE double precision arithmetic. The relative accuracy is better than $10^{-13}$ in the range $(0,200] \times [-200, 200]$ and close to $10^{-12}$ in $(0, 1500] \times [-1500, 1500]$.", acknowledgement = ack-nhfb, } @Article{Gil:2004:CSM, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing solutions of the modified {Bessel} differential equation for imaginary orders and positive arguments", journal = j-TOMS, volume = "30", number = "2", pages = "145--158", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/992200.992203", ISSN = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' + xw' + (a^2 - x^2)w = 0$. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.", acknowledgement = ack-nhfb, } @Misc{Kahan:2004:LTC, author = "W. Kahan", title = "A Logarithm Too Clever by Half", howpublished = "World-Wide Web document", pages = "9", day = "9", month = aug, year = "2004", bibdate = "Mon Apr 25 17:39:08 2005", URL = "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT", acknowledgement = ack-nhfb, remark = "Careful analysis of the problem of computing {\tt log10(x)} accurately from {\tt log(x)}.", } @Book{Lau:2004:NLJ, author = "H. T. (Hang Tong) Lau", title = "A numerical library in {Java} for scientists and engineers", publisher = pub-CHAPMAN-HALL-CRC, address = pub-CHAPMAN-HALL-CRC:adr, pages = "xxiii + 1063", year = "2004", ISBN = "1-58488-430-4", ISBN-13 = "978-1-58488-430-9", LCCN = "QA76.73.J38 L363 2004", bibdate = "Fri Sep 26 14:28:47 MDT 2008", bibsource = "z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0646/2003055149-d.html", acknowledgement = ack-nhfb, subject = "Java (Computer program language)", } @Article{Marsaglia:2004:END, author = "George Marsaglia", title = "Evaluating the Normal Distribution", journal = j-J-STAT-SOFT, volume = "11", number = "4", pages = "1--7", month = "", year = "2004", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sat Dec 04 09:18:40 2004", URL = "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1", accepted = "2004-07-18", acknowledgement = ack-nhfb, remark = "This article exhibits accurate, compact, and fast algorithms for computation of the normal distribution function and the complementary normal distribution, which have a simple relation to the error function and the complementary error function. They appear to be improvements on almost all previously-published algorithms for these functions. However, closer study shows that the complementary normal distribution function has an unchecked out-of-bounds array access for $|x| >= 17$, and its Taylor series sum has poor convergence because the tabulated intervals are twice too wide. The Taylor series sum for the normal distribution function is expanded around $x = 0$, and thus has poor convergence for large $|x|$. Neither function takes into account the accuracy loss when the computed result is the larger of the two (their sum is one, and their range is $[-\infty,+\infty]$), although the text discusses the problem. The article also discusses the historical origin of the term ``error function'', tracing it to J. W. Glaisher in 1871.", submitted = "2004-06-05", } @Article{Mathar:2004:NRI, author = "Richard J. Mathar", title = "Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument", journal = j-NUMER-ALGORITHMS, volume = "36", number = "3", pages = "247--264", month = jul, year = "2004", CODEN = "NUALEG", ISSN = "1017-1398", bibdate = "Mon Dec 6 07:00:32 MST 2004", bibsource = "http://www.kluweronline.com/issn/1017-1398", URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm", acknowledgement = ack-nhfb, } @InProceedings{Ortiz:2004:SPI, author = "I. Ortiz and M. Jimenez", booktitle = "MWSCAS '04. The 2004 47th Midwest Symposium on Circuits and Systems. 25--28 July 2004", title = "Scalable pipeline insertion in floating-point division and square root units", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "II-225--II-228", year = "2004", CODEN = "????", ISSN = "????", bibdate = "Sat Jul 16 15:28:14 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", abstract = "Division and square root are important operations in a number of data processing algorithms. They are inherently time consuming operations and can require a significant amount of resources when implemented in hardware. This work reports the development of scalable, floating-point (FP) division and square root operators with adjustable precision, range, and pipeline granularity. An algorithm for pipeline insertion was used for both operators, enabling speeds up to 204MFLOPS when implemented on a Xilinx Virtex II FPGA.", acknowledgement = ack-nhfb, summary = "Division and square root are important operations in a number of data processing algorithms. They are inherently time consuming operations and can require a significant amount of resources when implemented in hardware. This work reports the \ldots{}", } @Article{Pineiro:2004:AAL, author = "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D. Bruguera", title = "Algorithm and Architecture for Logarithm, Exponential and Powering Computation", journal = j-IEEE-TRANS-COMPUT, volume = "53", number = "9", pages = "1085--1096", year = "2004", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Fri Jun 24 10:05:48 2005", URL = "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps", acknowledgement = ack-nhfb, } @PhdThesis{Pugh:2004:ALG, author = "Glendon Ralpha Pugh", title = "An Analysis of the {Lanczos} Gamma Approximation", type = "Ph.D. thesis", school = "Department of Mathematics, University of British Columbia", address = "Vancouver, BC, Canada", pages = "viii + 154", month = "????", year = "2004", ISBN = "0-612-99536-4", ISBN-13 = "978-0-612-99536-9", LCCN = "AW5 .B7 2005-995364", bibdate = "Mon Nov 24 20:55:30 2008", acknowledgement = ack-nhfb, } @Article{VanDeun:2004:IAO, author = "J. {Van Deun} and A. Bultheel", title = "An Interpolation Algorithm for Orthogonal Rational Functions", journal = j-J-COMP-APPL-MATH, volume = "164--165", number = "??", pages = "749--762", month = mar, year = "2004", CODEN = "JCAMDI", DOI = "http://dx.doi.org/10.1016/S0377-0427(03)00493-X", ISSN = "0377-0427", bibdate = "Tue Mar 24 21:14:11 2009", note = "Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M.J. Goovaerts, S. Vandewalle, and L. Wuytack.", abstract = "Let $A=\{\alpha_1,\alpha_2,...\}$ be a sequence of numbers on the extended real line $\mathcal{R} = \mathcal{R} \union \{ \infty \}$ and $\mu$ a positive bounded Borel measure with support in (a subset of) $\mathcal{R}$. We introduce rational functions n with poles $\{\alpha_1,\ldots{},\alpha_n\}$ that are orthogonal with respect to $\mu$ (if all poles are at infinity, we recover the polynomial situation). It is well known that under certain conditions on the location of the poles, the system $\{\phi_n\}$ is regular such that the orthogonal functions satisfy a three-term recurrence relation similar to the one for orthogonal polynomials. To compute the recurrence coefficients one can use explicit formulas involving inner products. We present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the Riesz--Herglotz-Nevanlinna transform $\Omega_\mu$ of the measure $\mu$. Error bounds are derived and some examples serve as illustration.", acknowledgement = ack-nhfb, keywords = "orthogonal rational functions; orthogonal polynomials; three-term recurrence; interpolation", } @Article{Zhu:2004:ISR, author = "Hufei Zhu and Zhongding Lei and F. P. S. Chin", title = "An improved square-root algorithm for {BLAST}", journal = j-IEEE-SIGNAL-PROCESS-LETT, volume = "11", number = "9", pages = "772--775", month = sep, year = "2004", CODEN = "ISPLEM", ISSN = "1070-9908", bibdate = "Sat Jul 16 15:28:13 MDT 2005", bibsource = "http://ieeexplore.ieee.org/", acknowledgement = ack-nhfb, summary = "In this letter, an improved square-root algorithm for Bell Labs Layered Space-Time (BLAST) system is proposed. It speeds up the original square-root algorithm by 36% in terms of the number of multiplications and additions. Compared with the \ldots{}", } @InProceedings{Antelo:2005:LLD, author = "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi and Alberto Nannarelli", title = "Low Latency Digit-Recurrence Reciprocal and Square-Root Reciprocal Algorithm and Architecture", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-116.pdf", abstract = "The reciprocal and square-root reciprocal operations are important in several applications. For the operations, we present algorithms that combine a digit-by-digit module and one iteration of a quadratic-convergence approximation. The latter is implemented by a digit-recurrence, which uses the digits produced by the digit-by-digit part. In this way, both parts execute in an overlapped manner, so that the total number of cycles is about half the number that would be required by the digit-by-digit part alone. Because of the approximation, correct rounding of the result cannot be obtained directly in all cases; we propose a variable-time implementation that produces the correctly rounded result with a small average overhead. Radix-4 implementations are described and have been synthesized. They achieve the same cycle time as the standard digit-by-digit implementation, resulting in a speed-up of about 2 and, because of the approximation part, the area factor is also about 2. We also show a combined implementation for both operations that has essentially the same complexity as that for square-root reciprocal alone.", acknowledgement = ack-nhfb, pagecount = "8", } @Article{Brisebarre:2005:NRR, author = "Nicolas Brisebarre and David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol", title = "A New Range-Reduction Algorithm", journal = j-IEEE-TRANS-COMPUT, volume = "54", number = "3", pages = "331--339", month = mar, year = "2005", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Wed Apr 27 18:04:38 MDT 2005", bibsource = "http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm; http://ieeexplore.ieee.org/", URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf; http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197; http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.", abstract = "Range-reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double-precision range.", acknowledgement = ack-nhfb, } @InProceedings{deDinechin:2005:TPU, author = "Florent de Dinechin and Alexey Ershov and Nicolas Gast", title = "Towards the Post-ultimate {\tt libm}", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-165.pdf", abstract = "This article presents advances on the subject of correctly rounded elementary functions since the publication of the {\tt libultim} mathematical library developed by Ziv at IBM. This library showed that the average performance and memory overhead of correct rounding could be made negligible. However, the worst-case overhead was still a factor 1000 or more. It is shown here that, with current processor technology, this worst-case overhead can be kept within a factor of 2 to 10 of current best libms. This low overhead has very positive consequences on the techniques for implementing and proving correctly rounded functions, which are also studied. These results lift the last technical obstacles to a generalisation of (at least some) correctly rounded double precision elementary functions.", acknowledgement = ack-nhfb, pagecount = "8", } @Misc{IBM:2005:MAS, author = "{IBM Corporation}", title = "{Mathematical Acceleration Subsystem} for {Linux}", howpublished = "World Wide Web document", year = "2005", bibdate = "Mon Dec 05 18:59:35 2005", URL = "http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html", abstract = "Mathematical Acceleration Subsystem (MASS) for Linux consists of libraries of mathematical intrinsic functions tuned specifically for optimum performance on POWER architectures.", acknowledgement = ack-nhfb, keywords = "Mathematical Acceleration Subsystem (MASS)", remark = "Scalar library functions: atan, atan2, cos, cosh, dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh, sqrt, tan, and tanh.\par Vector library double-precision function: vacos, vasin, vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv, vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow, vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt, vtan, and vtanh.\par Vector library single-precision functions: vsacos, vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin, vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow, vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh, vssqrt, vstan, and vstanh.", } @Article{Kornerup:2005:DSS, author = "Peter Kornerup", title = "Digit Selection for {SRT} Division and Square Root", journal = j-IEEE-TRANS-COMPUT, volume = "54", number = "3", pages = "294--303", month = mar, year = "2005", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Tue Jul 19 09:20:54 MDT 2005", bibsource = "http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm; http://ieeexplore.ieee.org/", URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.; http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194", acknowledgement = ack-nhfb, summary = "The quotient digit selection in the SRT division algorithm is based on a few most significant bits of the remainder and divisor, where the remainder is usually represented in a redundant representation. The number of leading bits needed depends on \ldots{}", } @Article{Lee:2005:OHF, author = "D.-U. Lee and A. A. Gaffar and O. Mencer and W. Luk", title = "Optimizing hardware function evaluation", journal = j-IEEE-TRANS-COMPUT, volume = "54", number = "12", pages = "1520--1531", month = dec, year = "2005", CODEN = "ITCOB4", DOI = "http://dx.doi.org/10.1109/TC.2005.201", ISSN = "0018-9340", bibdate = "Tue May 30 12:04:26 2006", abstract = "We present a methodology and an automated system for function evaluation unit generation. Our system selects the best function evaluation hardware for a given function, accuracy requirements, technology mapping, and optimization metrics, such as area, throughput, and latency. Function evaluation $f(x)$ typically consists of range reduction and the actual evaluation on a small convenient interval such as $[0, \pi/2)$ for $\sin(x)$. We investigate the impact of hardware function evaluation with range reduction for a given range and precision of $x$ and $f(x)$ on area and speed. An automated bit-width optimization technique for minimizing the sizes of the operators in the data paths is also proposed. We explore a vast design space for fixed-point $\sin(x)$, $\log(x)$, and $\sqrt{x}$ accurate to one unit in the last place using MATLAB and ASC, a stream compiler for field-programmable gate arrays (FPGAs). In this study, we implement over 2,000 placed-and-routed FPGA designs, resulting in over 100 million application-specific integrated circuit (ASIC) equivalent gates. We provide optimal function evaluation results for range and precision combinations between 8 and 48 bits.", acknowledgement = ack-nhfb, keywords = "application specific integrated circuits; circuit optimisation; field programmable gate arrays; fixed point arithmetic; logic design; application specific integrated circuits; circuit optimisation; field programmable gate arrays; fixed point arithmetic; logic design; ASC; ASIC; FPGA; MATLAB; application-specific integrated circuit equivalent gates; automated bit-width optimization technique; computer arithmetic; elementary function approximation; field-programmable gate arrays; fixed-point arithmetic; hardware function evaluation optimisation; minimax approximation; stream compiler", } @InProceedings{Lefevre:2005:NRD, author = "Vincent Lef{\`e}vre", title = "New Results on the Distance Between a Segment and {$Z^2$}. Application to the Exact Rounding", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-147.pdf", abstract = "This paper presents extensions to Lef{\'e}vre's algorithm that computes a lower bound on the distance between a segment and a regular grid $Z^2$. This algorithm and, in particular, the extensions are useful in the search for worst cases for the exact rounding of unary elementary functions or base-conversion functions. The proof that is presented here is simpler and less technical than the original proof. This paper also gives benchmark results with various optimization parameters, explanations of these results, and an application to base conversion.", acknowledgement = ack-nhfb, pagecount = "8", } @InProceedings{Markstein:2005:FSM, author = "Peter Markstein", title = "A Fast-Start Method for Computing the Inverse Tangent", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-112.pdf", abstract = "In a search for an algorithm to compute $\atan(x)$ which has both low latency and few floating point instructions, an interesting variant of familiar trigonometry formulas was discovered that allow the start of argument reduction to commence before any references to tables stored in memory are needed. Low latency makes the method suitable for a closed subroutine, and few floating point operations make the method advantageous for a software-pipelined implementation.", acknowledgement = ack-nhfb, keywords = "IA-64; Itanium-2", pagecount = "6", } @Article{Pineiro:2005:HSF, author = "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and Jean-Michel Muller and Javier D. Bruguera", title = "High-Speed Function Approximation Using a Minimax Quadratic Interpolator", journal = j-IEEE-TRANS-COMPUT, volume = "54", number = "3", pages = "304--318", month = mar, year = "2005", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Tue Jul 19 09:20:54 MDT 2005", bibsource = "http://ieeexplore.ieee.org/; http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm", URL = "http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195; http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.; http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf", abstract = "A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent $p$), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).", acknowledgement = ack-nhfb, } @InProceedings{Stehle:2005:GAT, author = "Damien Stehl{\'e} and Paul Zimmermann", title = "{Gal}'s Accurate Tables Method Revisited", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-152.pdf", abstract = "Gal's accurate tables algorithm aims at providing an efficient implementation of mathematical functions with correct rounding as often as possible. This method requires an expensive pre-computation of the values taken by the function or by several related functions at some distinguished points. Our improvements of Gal's method are two-fold: on the one hand we describe what is the arguably best set of distinguished values and how it improves the efficiency and accuracy of the function implementation, and on the other hand we give an algorithm which drastically decreases the cost of the pre-computation. These improvements are related to the worst cases for the correct rounding of mathematical functions and to the algorithms for finding them. We demonstrate how the whole method can be turned into practice for $2^x$ and $\sin x$ for $x \in [1/2,1)$, in double precision.", acknowledgement = ack-nhfb, pagecount = "8", } @Article{Stehle:2005:SWC, author = "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul Zimmermann", title = "Searching Worst Cases of a One-Variable Function Using Lattice Reduction", journal = j-IEEE-TRANS-COMPUT, volume = "54", number = "3", pages = "340--346", month = mar, year = "2005", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Tue Jul 19 09:20:54 MDT 2005", bibsource = "http://ieeexplore.ieee.org/; http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm", URL = "http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198; http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.; http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf", abstract = "We propose a new algorithm to find worst cases for the correct rounding of a mathematical function of one variable. We first reduce this problem to the real small value problem---i.e., for polynomials with real coefficients. Then, we show that this second problem can be solved efficiently by extending Coppersmith's work on the integer small value problem---for polynomials with integer coefficients---using lattice reduction. For floating-point numbers with a mantissa less than $N$ and a polynomial approximation of degree $d$, our algorithm finds all worst cases at distance less than $N^{\frac{-d^2}{2d+1}}$ from a machine number in time $O(N^{{\frac{d+1}{2d+1}}+\varepsilon})$. For $d=2$, a detailed study improves on the $O(N^{2/3+\varepsilon})$ complexity from Lef{\`e}vre's algorithm to $O(N^{4/7+\varepsilon})$. For larger $d$, our algorithm can be used to check that there exist no worst cases at distance less than $N^{-k}$ in time $O(N^{1/2+\varepsilon})$.", acknowledgement = ack-nhfb, keywords = "Computer arithmetic; correct rounding; multiple precision arithmetic; special function approximations", } @InProceedings{Walters:2005:EFA, author = "George Walters and Michael Schulte", title = "Efficient Function Approximation Using Truncated Multipliers and Squarers", crossref = "IEEE:2005:PIS", pages = "??--??", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", URL = "http://arith17.polito.it/final/paper-190.pdf", abstract = "This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev series approximation, and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24-bits (IEEE single precision). Designs for linear and quadratic interpolators that implement the reciprocal function, $f(x) = 1/x,$ are presented and analyzed as an example. We show that a 24-bit truncated reciprocal quadratic interpolator with a design specification of $\pm 1$ ulp error requires 24.1\% fewer partial products to implement than a comparable standard interpolator with the same error specification.", acknowledgement = ack-nhfb, pagecount = "8", } @InProceedings{Anderson:2006:AMF, author = "Cristina S. Anderson and Shane Story and Nikita Astafiev", title = "Accurate Math Functions on the {Intel IA-32} Architecture: {A} Performance-Driven Design", crossref = "Anonymous:2006:PCR", pages = "??--??", year = "2006", bibdate = "Tue Jun 27 10:28:05 2006", acknowledgement = ack-nhfb, keywords = "elementary functions", } @InProceedings{deDinechin:2006:STP, author = "Florent de Dinechin and Sergey Maidanov", title = "Software techniques for perfect elementary functions in floating-point interval arithmetic", crossref = "Anonymous:2006:PCR", pages = "??--??", year = "2006", bibdate = "Tue Jun 27 10:28:05 2006", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Article{Gil:2006:ARP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 850}: {Real} parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "102--112", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1132973.1132978", ISSN = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions $U(a, x)$, $V(a, x)$ and their derivatives for real $a$ and $x ($x \geq 0)$. The code also computes scaled functions. The range of computation for scaled PCFs is practically unrestricted. The aimed relative accuracy for scaled functions is better than $5 \times 10^{14}$. Exceptions to this accuracy are the evaluation of the functions near their zeros and the error caused by the evaluation of trigonometric functions of large arguments when $|a| > x$. The routines always give values for which the Wronskian relation for scaled functions is verified with a relative accuracy better than $5 \times 10^{14}$. The accuracy of the unscaled functions is also better than $5 \times 10^{14}$ for moderate values of $x$ and $a$ (except close to the zeros), while for large $x$ and $a$ the error is dominated by exponential and trigonometric function evaluations. For IEEE standard double precision arithmetic, the accuracy is better than $5 \times 10^{13}$ in the computable range of unscaled PCFs (except close to the zeros).", acknowledgement = ack-nhfb, } @Article{Gil:2006:CRP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing the real parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "70--101", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1132973.1132977", ISSN = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "Methods for the computation of real parabolic cylinder functions $U(a, x)$, and $V(a, x)$ and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of the order $a$ and the variable $x$ except for the overflow\slash underflow limitations. By factoring the dominant exponential factor, scaled functions can be computed without practical overflow\slash underflow limitations. In an accompanying article we describe the precise domains for these methods and we present the Fortran 90 codes for the computation of these functions.", acknowledgement = ack-nhfb, } @InProceedings{Parks:2006:UTS, author = "Michael Parks", title = "Unifying Tests for Square Root", crossref = "Anonymous:2006:PCR", pages = "??--??", year = "2006", bibdate = "Tue Jun 27 10:28:05 2006", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Article{Wires:2006:RRS, author = "Kent E. Wires and Michael J. Schulte", title = "Reciprocal and Reciprocal Square Root Units with Operand Modification and Multiplication", journal = j-J-VLSI-SIGNAL-PROC, volume = "42", number = "3", pages = "257--272", month = mar, year = "2006", CODEN = "JVSPED", DOI = "http://dx.doi.org/10.1007/s11265-006-4186-0", ISSN = "0922-5773", bibdate = "Mon Mar 05 08:26:23 2007", URL = "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf", acknowledgement = ack-nhfb, } @InProceedings{Barnett:2007:HPV, author = "Ross Barnett and J. A. Youngman", booktitle = "{1st Joint Meeting of the American Mathematical Society and the New Zealand Mathematical Society, Victoria University of Wellington, Wellington, New Zealand, December 12--15, 2007}", title = "High-Precision Values of the Gamma Function of real argument", publisher = pub-AMS, address = pub-AMS:adr, pages = "????", year = "2007", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Mon Jul 14 11:57:00 2008", URL = "http://homepages.mcs.vuw.ac.nz/~mathmeet/amsnzms2007/abstracts.pdf", abstract = "A method is described to calculate values of $\Gamma(\nu)$, $0 \leq \nu \leq 1$ to arbitrary precision by combining a Bessel function with a $_0F_1$ function. Steed's algorithm is used to compute the regular Bessel function $J_\nu(x)$, for a suitable argument $x$ and real $\nu$, to arbitrary accuracy. Hence the gamma function is obtained. Example values are given to 200D. Verification is by the 80D-results of Frans{\'e}n and Wrigge, by the use of the duplication formula, and by computing the closed form results of Borwein and Zucker. A caveat is offered concerning the coding of the Bessel functions in Numerical Recipes and in the GSL library.", acknowledgement = ack-nhfb, } @Book{Gil:2007:NMS, author = "Amparo Gil and Javier Segura and N. M. Temme", title = "Numerical methods for special functions", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xvi + 415", year = "2007", ISBN-13 = "978-0-898716-34-4", LCCN = "QA351 .G455 2007", bibdate = "Fri Sep 14 10:24:22 MDT 2007", bibsource = "z3950.loc.gov:7090/Voyager", price = "US\$99.00", acknowledgement = ack-nhfb, remark = "To be published October 2007.", subject = "functions, special; data processing; numerical analysis; asymptotic expansions; approximation theory", } @Article{Kuliamin:2007:STI, author = "V. V. Kuliamin", title = "Standardization and testing of implementations of mathematical functions in floating point numbers", journal = j-PROG-COMP-SOFT, volume = "33", number = "3", pages = "154--173", year = "2007", DOI = "http://dx.doi.org/10.1134/S036176880703005X", ISSN = "0361-7688", bibdate = "Fri Aug 08 09:01:30 2008", abstract = "Requirements definition and test suites development for implementations of mathematical functions in floating point arithmetic in the framework of the IEEE 754 standard are considered. A method based on this standard is proposed for defining requirements for such functions. This method can be used for the standardization of implementations of such functions; this kind of standardization extends IEEE 754. A method for designing test suites for the verification of those requirements is presented. The proposed methods are based on specific properties of the representation of floating point numbers and on some features of the functions under examination.", acknowledgement = ack-nhfb, keywords = "floating-point function testing and verification", } @TechReport{Lefevre:2007:SNP, author = "Vincent Lef{\'e}vre and Jean-Michel Muller", title = "Some notes on the possible under\slash overflow of the most common elementary functions", type = "Report", institution = "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon", address = "Lyon, France", pages = "7", year = "2007", bibdate = "Fri May 25 16:18:32 2007", URL = "http://prunel.ccsd.cnrs.fr/ensl-00149414", abstract = "The purpose of this short note is not to describe when underflow or overflow must be signalled (it is quite clear that the rules are the same as for the basic arithmetic operations). We just want to show that for some of the most common functions and floating-point formats, in many cases, we can know in advance that the results will always lie in the range of the numbers that are representable by normal floating-point numbers, so that in these cases there is no need to worry about underflow or overflow. Note that when it is not the case, an implementation is still possible using a run-time test.", acknowledgement = ack-nhfb, keywords = "elementary functions; floating-point arithmetic; overflow; underflow", } @Article{Neher:2007:CSF, author = "Markus Neher", title = "Complex standard functions and their implementation in the {CoStLy} library", journal = j-TOMS, volume = "33", number = "1", pages = "??--??", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1206040.1206042", ISSN = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "The practical calculation of range bounds for some complex standard functions is addressed in this article. The functions under consideration are root and power functions, the exponential, trigonometric and hyperbolic functions, and their inverse functions. For such a function $f$ and a given rectangular complex interval $z$, some interval $w$ is computed that contains all function values of $f$ in $z$. This is done by expressing the real and the imaginary part of $f$ as compositions of real standard functions and then estimating the ranges of these compositions. In many cases, the inclusions are optimal, such that $w$ is the smallest rectangular interval containing the range of $f$. The algorithms presented in this article have been implemented in a C++ class library called CoStLy (Complex Standard Functions License), which is distributed under the conditions of the GNU General Public License.", acknowledgement = ack-nhfb, articleno = "2", } @Article{Schmelzer:2007:CGF, author = "Thomas Schmelzer and Lloyd N. Trefethen", title = "Computing the Gamma Function Using Contour Integrals and Rational Approximations", journal = j-SIAM-J-NUMER-ANAL, volume = "45", number = "2", pages = "558--571", month = "????", year = "2007", CODEN = "SJNAAM", DOI = "http://dx.doi.org/10.1137/050646342", ISSN = "0036-1429 (print), 1095-7170 (electronic)", bibdate = "Mon Nov 24 18:03:07 MST 2008", bibsource = "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=45&Issue=2", acknowledgement = ack-nhfb, } @Article{Kodama:2008:ASP, author = "Masao Kodama", title = "{Algorithm 877}: {A} Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument", journal = j-TOMS, volume = "34", number = "4", pages = "22:1--22:21", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/1377596.1377602", ISSN = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", abstract = "The algorithm presented provides a package of subroutines for calculating the cylindrical functions $J_\nu(x)$, $N_\nu(x)$, $H_\nu^{1}(x)$, $H_\nu^{2}(x)$ where the order $\nu$ is complex and the real argument $x$ is nonnegative. The algorithm is written in Fortran 95 and calculates the functions using single, double, or quadruple precision according to the value of a parameter defined in the algorithm. The methods of calculating the functions are based on a series expansion, Debye's asymptotic expansions, Olver's asymptotic expansions, and recurrence methods (Miller's algorithms). The relative errors of the functional values computed by this algorithm using double precision are less than $2.4 \times 10^{-13}$ in the region $0 \leq \mbox{Re}(\nu) \leq 64$, $0 \leq \mbox{Im}(\nu) \leq 63$, $0.024 \leq x \leq 97$.", acknowledgement = ack-nhfb, articleno = "22", keywords = "Bessel functions; complex order; Cylindrical functions; Debye's asymptotic expansions; Hankel functions; Miller's algorithms; Neumann functions; nonnegative argument; numerical calculation; Olver's asymptotic expansions", } @Article{Harris:2009:MIB, author = "Frank E. Harris and J. G. Fripiat", title = "Methods for incomplete {Bessel} function evaluation", journal = j-IJQC, volume = "109", number = "8", pages = "1728--1740", month = feb, year = "2009", CODEN = "IJQCB2", DOI = "http://dx.doi.org/10.1002/qua.21972", ISSN = "0020-7608", bibdate = "Fri Mar 27 07:41:18 2009", abstract = "Presented here are detailed methods for evaluating the incomplete Bessel functions arising when Gaussian-type orbitals are used for systems periodic in one spatial dimension. The scheme is designed to yield these incomplete Bessel functions with an absolute accuracy of $\pm 1 \times 10^{-10}, for the range of integer orders $0 \leq n \leq 12$ [a range sufficient for a basis whose members have angular momenta of up to three units ($s$, $p$, $d$, or $f% atomic functions)]. To reach this accuracy level within acceptable computation times, new rational approximations were developed to compute the special functions involved, namely, the exponential integral $E_1(x)$ and the modified Bessel functions $K_0(x)$ and $K_1(x)$, to absolute accuracy $\pm 1 \time 10^{-15}.", acknowledgement = ack-nhfb, keywords = "E1(x); incomplete Bessel function; K0(x); K1(x); leaky aquifer function; modified Bessel function; exponential integral; numerical methods", } @Article{Weniger:2009:SHF, author = "Ernst Joachim Weniger", title = "The strange history of {$B$} functions or how theoretical chemists and mathematicians do (not) interact", journal = j-IJQC, volume = "109", number = "8", pages = "1728--1740", month = feb, year = "2009", CODEN = "IJQCB2", DOI = "http://dx.doi.org/10.1002/qua.22014", ISSN = "0020-7608", bibdate = "Fri Mar 27 07:47:31 2009", abstract = "$B$ functions are a class of relatively complicated exponentially decaying basis functions. Because the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why $B$ functions should offer any advantages. However, $B$ functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of $B$ functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.", acknowledgement = ack-nhfb, keywords = "electronic structure theory; exponentially decaying basis functions; B functions; multicenter integrals; interdisciplinary collaboration", } %%% ==================================================================== %%% Cross-referenced entries must come last: @Book{Ralston:1960:MMD, editor = "Anthony Ralston and Herbert S. Wilf", booktitle = "Mathematical methods for digital computers", title = "Mathematical methods for digital computers", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "various", year = "1960--1977", ISBN = "0-471-70690-6", ISBN-13 = "978-0-471-70690-8", LCCN = "QA39 .R26", bibdate = "Mon Jan 13 10:36:06 1997", note = "Three volumes.", acknowledgement = ack-nhfb, } @Proceedings{AFIPS:1969:ACPb, key = "AFIPS FJCC '69", title = "1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada", volume = "35", publisher = pub-AFIPS, address = pub-AFIPS:adr, pages = "807", year = "1969", LCCN = "TK7885.A1 J6 1969", bibdate = "Sat Sep 24 01:06:00 1994", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", series = "AFIPS conference proceedings", acknowledgement = ack-nhfb, } @Proceedings{AFIPS:1971:ACP, key = "AFIPS SJCC '71", booktitle = "1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey", title = "1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey", volume = "38", publisher = pub-AFIPS, address = pub-AFIPS:adr, pages = "631", year = "1971", LCCN = "????", bibdate = "Fri Sep 16 10:47:01 1994", series = "AFIPS conference proceedings", acknowledgement = ack-nj, } @Book{Rice:1971:MS, author = "John R. Rice", booktitle = "Mathematical Software", title = "Mathematical Software", publisher = pub-AP, address = pub-AP:adr, pages = "xvii + 515", year = "1971", ISBN = "0-12-587250-X", ISBN-13 = "978-0-12-587250-8", LCCN = "QA1 .M26", bibdate = "Thu Sep 15 18:56:52 1994", note = "Based on the proceedings of the Mathematical Software Symposium held at Purdue University, Lafayette, Indiana, USA, April 1--3, 1970.", acknowledgement = ack-nhfb, } @Proceedings{Miller:1975:TNA, editor = "John J. H. Miller", booktitle = "Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976", title = "Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976", publisher = pub-AP, address = pub-AP:adr, pages = "various", year = "1975", ISBN = "0-12-496950-X", ISBN-13 = "978-0-12-496950-6", LCCN = "QA297 .R69 1973", bibdate = "Mon Jan 13 10:41:13 1997", acknowledgement = ack-nhfb, } @Proceedings{Traub:1976:ACC, editor = "J. F. (Joseph Frederick) Traub", booktitle = "{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}", title = "{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}", publisher = pub-AP, address = pub-AP:adr, pages = "ix + 239", year = "1976", ISBN = "0-12-697560-4", ISBN-13 = "978-0-12-697560-4", LCCN = "QA297.S9151 1975", bibdate = "Mon Jan 13 10:18:33 1997", acknowledgement = ack-nhfb, } @Proceedings{IEEE:1978:PSC, editor = "{IEEE}", booktitle = "Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, CA)", title = "Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, {CA})", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xi + 274", year = "1978", ISSN = "1063-6889", LCCN = "QA76.6 .S919a", bibdate = "Mon May 19 15:22:15 1997", note = "IEEE catalog no. 78 CH1412-6C.", acknowledgement = ack-nhfb, keywords = "Electronic digital computers --- Programming --- Congresses.; Floating-point arithmetic --- Congresses.; Computer arithmetic --- Congresses.", } @Proceedings{Alefeld:1980:PSE, editor = "G. Alefeld and R. D. Grigorieff and R. Albrecht and U. Kulisch and F. Stummel", booktitle = "Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin", title = "Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin", volume = "2", publisher = pub-SV, address = pub-SV:adr, pages = "229", year = "1980", ISBN = "0-387-81566-X", ISBN-13 = "978-0-387-81566-4", ISSN = "0344-8029", LCCN = "QA297 .F84", bibdate = "Mon Jan 13 10:20:47 1997", series = "Computing. Supplementum", acknowledgement = ack-nhfb, } @Proceedings{Lavington:1980:IPP, editor = "Simon Hugh Lavington", booktitle = "Information Processing 80: Proceedings of {IFIP} Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980", title = "Information Processing 80: Proceedings of {IFIP} Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980", publisher = pub-ENH, address = pub-ENH:adr, pages = "xiii + 1070", year = "1980", ISBN = "0-444-86034-7", ISBN-13 = "978-0-444-86034-7", LCCN = "QA 75.5 I57 1980", bibdate = "Thu Sep 01 23:09:20 1994", acknowledgement = ack-nhfb, } @Proceedings{IEEE:1981:PIS, editor = "{IEEE}", booktitle = "Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan", title = "Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "vii + 278", year = "1981", LCCN = "QA76.9.C62 S95 1981", bibdate = "Mon May 19 13:17:13 1997", note = "IEEE Catalog No. 81CH1630-3. Computer Society Order No. 347.", acknowledgement = ack-nhfb, xxISBN = "none", } @Proceedings{Mulvey:1982:EMP, editor = "J. M. Mulvey", title = "Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards, Boulder, Colorado, January 5--6, 1981", volume = "199", publisher = pub-SV, address = pub-SV:adr, pages = "xi + 379", year = "1982", ISBN = "0-387-11495-5", ISBN-13 = "978-0-387-11495-8", LCCN = "QA402.5 .E94 1982", bibdate = "Thu Nov 17 06:36:49 1994", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", series = "Lecture Notes in Economics and Mathematical Systems", acknowledgement = ack-nhfb, } @Book{Bultheel:1999:ORF, editor = "Adhemar Bultheel and Pablo Gonzales-Vera and Erik Hendriksen and Olav Njastad", booktitle = "Orthogonal Rational Functions", title = "Orthogonal Rational Functions", volume = "5", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xiv + 407", year = "1999", ISBN = "0-521-65006-2 (hardcover)", ISBN-13 = "978-0-521-65006-9 (hardcover)", LCCN = "QA404.5 .O75 1999", bibdate = "Tue Mar 24 21:04:21 MDT 2009", bibsource = "z3950.loc.gov:7090/Voyager", series = "Cambridge monographs on applied and computational mathematics", URL = "http://www.loc.gov/catdir/toc/cam024/98011646.html; http://www.loc.gov/catdir/description/cam029/98011646.html", acknowledgement = ack-nhfb, subject = "functions, orthogonal; functions of complex variables", } @Proceedings{Marron:1985:FEP, editor = "J. S. Marron", title = "Function estimates: proceedings of a conference held July 28--August 3, 1985", volume = "59", publisher = pub-AMS, address = pub-AMS:adr, pages = "ix + 178", year = "1985", ISBN = "0-8218-5062-8", ISBN-13 = "978-0-8218-5062-6", ISSN = "0271-4132", LCCN = "QA276.8 .C651 1985", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", note = "Held at Humboldt State University, Arcata, California.", series = "Contemporary mathematics (American Mathematical Society)", acknowledgement = ack-nhfb, bibno = "18241", catcode = "G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "algorithms; theory", guideno = "1986-12215", procdate = "July 28--Aug. 3, 1985", procloc = "Arcata, CA", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Proceedings{Miranker:1985:ASC, editor = "Willard L. Miranker and Richard A. Toupin", booktitle = "Accurate Scientific Computations: Symposium, Bad Neuenahr, {FRG}, March 12--14, 1985: Proceedings", title = "Accurate Scientific Computations: Symposium, Bad Neuenahr, {FRG}, March 12--14, 1985: Proceedings", volume = "235", publisher = pub-SV, address = pub-SV:adr, pages = "x + 205", year = "1985", ISBN = "0-387-16798-6", ISBN-13 = "978-0-387-16798-5", LCCN = "QA76.95 .A231 1986", bibdate = "Mon May 19 12:34:16 1997", series = "Lecture Notes in Computer Science", acknowledgement = ack-nhfb, } @Proceedings{Miranker:1986:ASC, editor = "Willard L. Miranker and Richard A. Toupin", booktitle = "Accurate scientific computations: symposium, Bad Neuenahr, {FRG}, March 12--14, 1985: proceedings", title = "Accurate scientific computations: symposium, Bad Neuenahr, {FRG}, March 12--14, 1985: proceedings", volume = "235", publisher = pub-SV, address = pub-SV:adr, pages = "x + 205", year = "1986", CODEN = "LNCSD9", ISBN = "0-387-16798-6 (USA: paperback)", ISBN-13 = "978-0-387-16798-5 (USA: paperback)", ISSN = "0302-9743", LCCN = "QA76.95 .A231 1986", bibdate = "Fri Apr 12 07:14:49 1996", note = "Symposium sponsored by IBM Deutschland.", series = ser-LNCS, acknowledgement = ack-nhfb, keywords = "mathematics --- data processing --- congresses; numerical calculations --- congresses", } @Proceedings{ACM:1987:UAA, editor = "{ACM}", booktitle = "Using Ada: ACM SIGAda international conference, Boston, Massachusetts, December 8--11, 1987", title = "Using Ada: {ACM} {SIGA}da international conference, Boston, Massachusetts, December 8--11, 1987", publisher = pub-ACM, address = pub-ACM:adr, pages = "viii + 240", year = "1987", ISBN = "0-89791-243-8", ISBN-13 = "978-0-89791-243-3", LCCN = "QA 76.73 A35 U85 1987", bibdate = "Mon May 19 13:18:54 1997", acknowledgement = ack-nhfb, } @Proceedings{Iserles:1987:SAN, editor = "A. Iserles and M. J. D. Powell", booktitle = "The State of the Art in Numerical Analysis: Proceedings of the Joint {IMA}\slash {SIAM} Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986", title = "The State of the Art in Numerical Analysis: Proceedings of the Joint {IMA}\slash {SIAM} Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xiv + 719", year = "1987", ISBN = "0-19-853614-3", ISBN-13 = "978-0-19-853614-7", LCCN = "QA297 .S781 1987", bibdate = "Thu Sep 08 00:41:24 1994", price = "UK\pounds55.00, US\$77.50", acknowledgement = ack-nj, } @Proceedings{Mason:1987:AA, editor = "J. C. Mason and M. G. Cox", booktitle = "Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985", title = "Algorithms for approximation: based on the proceedings of the {IMA} Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985", volume = "10", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xvi + 694", year = "1987", ISBN = "0-19-853612-7", ISBN-13 = "978-0-19-853612-3", LCCN = "QA221 .A5361 1987", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991)", price = "US\$90", series = "The Institute of Mathematics and Its Applications conference series, new series", acknowledgement = ack-nhfb, bibno = "39820", catcode = "G.1.2; G.1.2", CRclass = "G.1.2 Approximation; G.1.2 Approximation; G.1.2 Elementary function approximation", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation", genterm = "theory; algorithms", guideno = "1987-16080", procdate = "The Institute of mathematics and its applications conference series; 10 July 1985", procloc = "Shrivenham, UK", sub = "Proceedings of the IMA Conference on Algorithms for the approximation of functions", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", } @Proceedings{USENIX:1988:UPC, editor = "{USENIX Association}", booktitle = "{USENIX} proceedings: {C++} Conference, Denver, {CO}, October 17--21, 1988", title = "{USENIX} proceedings: {C++} Conference, Denver, {CO}, October 17--21, 1988", publisher = pub-USENIX, address = pub-USENIX:adr, pages = "362", year = "1988", bibdate = "Sun Feb 18 07:46:09 MST 1996", acknowledgement = ack-nhfb, keywords = "C++ (Computer program language) --- Congresses.", } @Proceedings{ACM:1989:PAI, editor = "{ACM}", booktitle = "Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC '89", title = "Proceedings of the {ACM}-{SIGSAM} 1989 International Symposium on Symbolic and Algebraic Computation, {ISSAC} '89", publisher = pub-ACM, address = pub-ACM:adr, pages = "399", year = "1989", ISBN = "0-89791-325-6", ISBN-13 = "978-0-89791-325-6", LCCN = "QA76.95.I59 1989", bibdate = "Tue Sep 17 06:46:18 MDT 1996", acknowledgement = ack-nhfb, confdate = "17--19 July 1989", conflocation = "Portland, OR, USA", confsponsor = "ACM", pubcountry = "USA", } @Proceedings{Ercegovac:1989:PSC, editor = "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander, Jr.}", booktitle = "Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, {USA}", title = "Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, {USA}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xv + 247", year = "1989", ISBN = "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)", ISBN-13 = "978-0-8186-8963-5 (case), 978-0-8186-5963-8 (microfiche)", LCCN = "QA 76.9 C62 S95 1989", bibdate = "Thu Sep 01 22:36:52 1994", note = "IEEE catalog no. 89CH2757-3.", acknowledgement = ack-nhfb, confdate = "6-8 Sept. 1989", conflocation = "Santa Monica, CA, USA", confsponsor = "IEEE; IFIP; Univ. California", pubcountry = "USA", } @Proceedings{Megiddo:1989:PMP, editor = "N. Megiddo", booktitle = "Progress in Mathematical Programming: Interior-Point and Related Methods", title = "Progress in Mathematical Programming: Interior-Point and Related Methods", publisher = pub-SV, address = pub-SV:adr, pages = "x + 158", year = "1989", ISBN = "0-387-96847-4", ISBN-13 = "978-0-387-96847-6", LCCN = "QA402.5 .P7851 1989", bibdate = "Sat Nov 09 07:07:37 2002", note = "Proceedings of the conference held at the Asilomar conference center in Pacific Grove, California, March 1--4, 1987.", acknowledgement = ack-nhfb, } @Book{Srivastava:1989:UFF, editor = "H. M. Srivastava and Shigeyoshi Owa", booktitle = "Univalent functions, fractional calculus, and their applications (K\=oriyama, 1988)", title = "Univalent functions, fractional calculus, and their applications ({K}\=oriyama, 1988)", publisher = pub-ELLIS-HORWOOD, address = pub-ELLIS-HORWOOD:adr, pages = "404", year = "1989", ISBN = "0-470-21630-1, 0-7458-0701-0 (??invalid ISBN checksum??)", ISBN-13 = "978-0-470-21630-9, 978-0-7458-0701-0 (??invalid ISBN-13 checksum??)", LCCN = "QA331 .U55 1989", bibdate = "Mon Jan 13 09:52:29 1997", price = "UK\pounds 39.95", acknowledgement = ack-nhfb, } @Proceedings{Cray:1990:PCU, editor = "????", key = "Cray UG '90", booktitle = "Proceedings Cray User Group", title = "Proceedings Cray User Group", publisher = "????", address = "????", pages = "????", month = "Spring", year = "1990", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Thu Sep 08 08:56:01 1994", acknowledgement = ack-nj, } @Proceedings{Anonymous:1991:PIS, editor = "Anonymous", booktitle = "Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991", title = "Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991", publisher = "Kyushu University Press", address = "Fukuoka, Japan", pages = "iv + 261", year = "1991", ISBN = "4-87378-284-8", ISBN-13 = "978-4-87378-284-3", LCCN = "QA76.88.I 1991", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, searchkey = "ti:elementary function", } @Proceedings{IEEE:1991:PSA, editor = "{IEEE}", booktitle = "Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991", title = "Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xxiii + 917", year = "1991", ISBN = "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper), 0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)", ISBN-13 = "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE paper), 978-0-8186-6158-7 (IEEE microfiche), 978-0-89791-459-8 (ACM)", LCCN = "QA76.5 .S894 1991", bibdate = "Fri Aug 30 08:01:51 MDT 1996", bibsource = "University of California MELVYL catalog.", note = "ACM order number 415913. IEEE Computer Society Press order number 2158. IEEE catalog number 91CH3058-5.", acknowledgement = ack-nhfb, classification = "C5440 (Multiprocessor systems and techniques); C5470 (Performance evaluation and testing); C6110P (Parallel programming)", keywords = "combinatorial algorithms; data dependence; distributed memory code generation; high school environment; latency tolerance; memory access; numerical algorithms; parallel processing; parallel programming; performance evaluation; performance tools; processor design; program analysis; storage hierarchy optimization; supercomputer benchmarks; supercomputer congresses; supercomputing; system issues", } @Proceedings{Kornerup:1991:PIS, editor = "Peter Kornerup and David W. Matula", booktitle = "Proceedings: 10th {IEEE} Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France", title = "Proceedings: 10th {IEEE} Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xiii + 282", year = "1991", ISBN = "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche), 0-7803-0187-0 (library binding)", ISBN-13 = "978-0-8186-9151-5 (case), 978-0-8186-6151-8 (microfiche), 978-0-7803-0187-0 (library binding)", LCCN = "QA76.9.C62 S95 1991", bibdate = "Thu Sep 01 23:18:52 1994", acknowledgement = ack-nhfb, } @Proceedings{EC2:1992:DJN, key = "AEF'92", title = "Deuxi{\`e}mes journ{\'e}es nationales: Les applications des ensembles flous, en l'honneur du {Professeur A. Kaufmann}, {Nimes}, 2--3 novembre 1992, conference scientifique ({English}: Second national conference: Application of Fuzzy Sets, in honor of {Professor A. Kaufman}, {Nimes}, 2--3 {November} 1992, scientific conference)", publisher = "EC2", address = "Nanterre Cedex, France", pages = "384", year = "1992", ISBN = "2-906899-78-X", ISBN-13 = "978-2-906899-78-0", LCCN = "????", bibdate = "Wed Jan 10 07:40:53 1996", acknowledgement = ack-nhfb, } @Book{Adams:1993:ACA, editor = "E. Adams and U. Kulisch", booktitle = "Scientific computing with automatic result verification", title = "Scientific computing with automatic result verification", volume = "189", publisher = pub-AP, address = pub-AP:adr, pages = "x + 612", year = "1993", ISBN = "0-12-044210-8", ISBN-13 = "978-0-12-044210-2", LCCN = "QA76.S368 1993", bibdate = "Mon Jan 13 09:58:58 1997", series = "Mathematics in science and engineering", acknowledgement = ack-nhfb, } @Proceedings{Sincovec:1993:PSS, editor = "Richard F. Sincovec and others", title = "Proceedings of the Sixth {SIAM} Conference on Parallel Processing for Scientific Computing, held March 22--24, 1993, in Norfolk, {VA}, {USA}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xix + 1041 + iv", year = "1993", ISBN = "0-89871-315-3", ISBN-13 = "978-0-89871-315-2", LCCN = "QA76.58 .S55 1993 v.1-2", bibdate = "Tue Oct 11 12:21:40 1994", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Two volumes.", } @Proceedings{Swartzlander:1993:SCA, editor = "Earl {Swartzlander, Jr.} and Mary Jane Irwin and Graham Jullien", booktitle = "Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario", title = "Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xii + 284", year = "1993", ISBN = "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound), 0-8186-3861-3 (microfiche)", ISBN-13 = "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6 (casebound), 978-0-8186-3861-9 (microfiche)", ISSN = "0018-9340", LCCN = "QA 76.9 C62 S95 1993", bibdate = "Thu Sep 01 22:58:49 1994", note = "IEEE Transactions on Computers {\bf 43(8)}, 1994", acknowledgement = ack-nhfb, } @Proceedings{Cuyt:1994:NNM, editor = "Annie Cuyt", booktitle = "Nonlinear numerical methods and rational approximation {II}", title = "Nonlinear numerical methods and rational approximation {II}", volume = "296", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "xviii + 446", year = "1994", ISBN = "0-7923-2967-8", LCCN = "QA297 .N642 1994", bibdate = "Wed Nov 3 09:30:14 MST 1999", note = "Proceedings of an international conference held at the University of Antwerp, Belgium, Sept. 5--11, 1993.", series = "Mathematics and its applications", acknowledgement = ack-nhfb, keywords = "approximation theory -- congresses; numerical analysis -- congresses", } @Proceedings{Gautschi:1994:MCH, editor = "Walter Gautschi", booktitle = "{Mathematics of Computation} 1943--1993: a half-century of computational mathematics", title = "{Mathematics of Computation} 1943--1993: a half-century of computational mathematics", volume = "48", publisher = pub-AMS, address = pub-AMS:adr, pages = "xx + 643", year = "1994", ISBN = "0-8218-0291-7", ISBN-13 = "978-0-8218-0291-5", MRclass = "00B25 (11-06 65-06)", MRnumber = "95j:00014", note = "Papers from the Symposium on Numerical Analysis and the Minisymposium on Computational Number Theory held in Vancouver, British Columbia, August 9--13, 1993", series = "Proceedings of Symposia in Applied Mathematics", } @Proceedings{Mudge:1994:PTS, editor = "Trevor N. Mudge and Bruce D. Shriver", booktitle = "Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. I: Architecture", title = "Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. {I}: Architecture", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "various", year = "1994", ISBN = "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)", ISBN-13 = "978-0-8186-5050-5 (paper), 978-0-8186-5051-2 (microfiche)", LCCN = "????", bibdate = "Mon Jan 13 10:02:18 1997", note = "First of five volumes. IEEE Catalog No. 94TH0607-2.", acknowledgement = ack-nhfb, } @Proceedings{Knowles:1995:PSC, editor = "Simon Knowles and William H. McAllister", booktitle = "Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England", title = "Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xvi + 252", year = "1995", ISBN = "0-8186-7089-4 (paperback), 0-8186-7089-4 (case), 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound), 0-7803-2949-X (casebound)", ISBN-13 = "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3 (case), 978-0-8186-7149-4 (microfiche), 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2 (casebound)", LCCN = "QA 76.9 C62 S95 1995", bibdate = "Sun Mar 29 08:48:20 1998", acknowledgement = ack-nhfb, } @Proceedings{Singh:1995:CRT, editor = "Avtar Singh", booktitle = "Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems \& Computers: October 30--November 1, 1995 Pacific Grove, California", title = "Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems \& Computers: October 30--November 1, 1995 Pacific Grove, California", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "various", year = "1995", ISBN = "0-8186-7370-2", ISBN-13 = "978-0-8186-7370-2", LCCN = "TK7801 .A83 1995", bibdate = "Sun Mar 29 08:51:26 1998", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Boisvert:1997:QNS, editor = "Ronald F. Boisvert", booktitle = "Quality of Numerical Software: Assessment and Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996}", title = "Quality of Numerical Software: Assessment and Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996}", publisher = pub-CHAPMAN-HALL, address = pub-CHAPMAN-HALL:adr, pages = "vii + 384", year = "1997", ISBN = "0-412-80530-8", ISBN-13 = "978-0-412-80530-1", LCCN = "QA297 .I35 1996", bibdate = "Fri Jul 09 05:58:30 2004", acknowledgement = ack-nhfb, } @Proceedings{Lang:1997:ISC, editor = "Tomas Lang and Jean-Michel Muller and Naofumi Takagi", booktitle = "13th IEEE Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, USA", title = "13th {IEEE} Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, {USA}", volume = "13", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xiii + 291", year = "1997", ISBN = "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8", ISBN-13 = "978-0-8186-7846-2, 978-0-8186-7847-9, 978-0-8186-7848-6", ISSN = "1063-6889", LCCN = "QA76.9.C62 S95 1997", bibdate = "Fri Mar 27 09:56:17 MST 1998", note = "IEEE Computer Society order number PR07846. IEEE Order Plan catalog number 97CB36091.", series = "Symposium on Computer Arithmetic", acknowledgement = ack-nhfb, sponsor = "IEEE.", } @Proceedings{Thiele:1997:IIC, editor = "Lothar Thiele and others", booktitle = "{IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Z{\"u}rich, Switzerland}", title = "{IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Z{\"u}rich, Switzerland}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xii + 540", year = "1997", ISBN = "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1", ISBN-13 = "978-0-8186-7959-9, 978-0-8186-7960-5, 978-0-8186-7958-2", LCCN = "TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6 .I58 1997", bibdate = "Sun Mar 4 21:13:29 MST 2007", bibsource = "melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, meetingname = "International Conference on Application-Specific Systems, Architectures, and Processors (11th : 1997 : Z{\"u}rich, Switzerland)", remark = "IEEE Computer Society Press order number PR07958. IEEE catalog number 97TB100177", subject = "Array processors; Congresses; Signal processing; Digital techniques; Application-specific integrated circuits", } @Proceedings{IEEE:1999:PIF, editor = "IEEE", booktitle = "Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland", title = "Proceedings of the {IEEE} Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xi + 217", year = "1999", ISBN = "0-7695-0219-9", ISBN-13 = "978-0-7695-0219-9", LCCN = "ZA4080 .F67 1999", bibdate = "Fri Jul 09 06:32:32 2004", acknowledgement = ack-nhfb, xxeditor = "Frances M. Titsworth", } @Proceedings{Koren:1999:ISC, editor = "Israel Koren and Peter Kornerup", booktitle = "14th IEEE Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia", title = "14th {IEEE} Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xi + 274", year = "1999", ISBN = "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4", ISBN-13 = "978-0-7803-5609-2, 978-0-7695-0116-1, 978-0-7695-0118-5", ISSN = "1063-6889", LCCN = "QA76.6 .S887 1999", bibdate = "Mon Feb 7 07:28:26 MST 2000", note = "IEEE Computer Society Order Number PR00116. IEEE Order Plan Catalog Number 99CB36336.", URL = "http://computer.org/conferen/home/arith/; http://www.ecs.umass.edu/ece/arith14/program.html", acknowledgement = ack-nhfb, annote = "Also known as ARITH-14.", source = "Computer arithmetic", sponsor = "IEEE.", } @Proceedings{Luk:1999:PSA, editor = "Franklin T. Luk", booktitle = "Proceedings of {SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado}", title = "Proceedings of {SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado}", volume = "3807", publisher = pub-SPIE, address = pub-SPIE:adr, pages = "ix + 648", year = "1999", ISBN = "0-8194-3293-8", ISBN-13 = "978-0-8194-3293-3", LCCN = "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9 .A37 1999; TK5102.5; TS510 .S63", bibdate = "Mon Mar 5 07:43:43 MST 2007", bibsource = "melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, subject = "Signal processing; Digital techniques; Congresses; Algorithms; Computer architecture", } @Proceedings{Dunkl:2000:PIW, editor = "Charles Dunkl and Mourad Ismail and Roderick Wong", booktitle = "Proceedings of the international workshop, special functions: {Hong Kong, 21--25 June 1999}", title = "Proceedings of the international workshop, special functions: {Hong Kong, 21--25 June 1999}", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xi + 438", year = "2000", ISBN = "981-02-4393-6", ISBN-13 = "978-981-02-4393-7", LCCN = "QA351 .P76 2000", bibdate = "Fri Jul 09 06:30:25 2004", acknowledgement = ack-nhfb, } @Proceedings{Sprague:2000:PAH, editor = "Ralph H. Sprague", booktitle = "{Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii}", title = "{Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "liv + 259", year = "2000", ISBN = "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7", ISBN-13 = "978-0-7695-0493-3, 978-0-7695-0494-0, 978-0-7695-0495-7", LCCN = "TA168 .H37 2000; TA168 .H37 2000xeb; TA168", bibdate = "Sun Mar 4 21:23:42 MST 2007", bibsource = "melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, meetingname = "Hawaii International Conference on System Sciences (33rd : 2000 : Maui, Hawaii)", remark = "IEEE Computer Society Order Number: PR00493", subject = "Systems engineering; Congresses; Information theory; Electronic data processing; System design", } @Proceedings{Burgess:2001:ISC, editor = "N. Burgess and L. Ciminiera", booktitle = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001}", title = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xii + 285", year = "2001", ISBN = "0-7695-1150-3; 0-7695-1152-X", ISBN-13 = "978-0-7695-1150-4; 978-0-7695-1152-8", ISSN = "1063-6889", LCCN = "????", bibdate = "Fri May 03 14:20:49 2002", note = "IEEE order no. PR01150.", price = "US\$145", acknowledgement = ack-nhfb, xxnote = "Check dates: 11--13 or 11--17??", xxtitle = "Computer Arithmetic: Papers presented at the {15th IEEE Symposium on Computer Arithmetic (Arith-15 2001), 11--17 June, 2001, Vail, CO}", } @Book{Lide:2001:CEM, editor = "David R. Lide", booktitle = "A Century of Excellence in Measurements, Standards, and Technology", title = "A Century of Excellence in Measurements, Standards, and Technology", volume = "958", publisher = pub-NIST, address = pub-NIST:adr, pages = "ix + 386", year = "2001", bibdate = "Fri Jul 09 06:29:11 2004", series = "NIST special publication", acknowledgement = ack-nhfb, } @Book{Lide:2002:CEM, editor = "David R. Lide", booktitle = "A Century of Excellence in Measurements, Standards, and Technology", title = "A Century of Excellence in Measurements, Standards, and Technology", publisher = pub-CRC, address = pub-CRC:adr, pages = "ix + 386", year = "2002", ISBN = "0-8493-1247-7", ISBN-13 = "978-0-8493-1247-2", LCCN = "QC100.U6 .C46 2002", bibdate = "Fri Jul 09 06:29:11 2004", note = "Republication of \cite{Lide:2001:CEM}.", URL = "http://www.loc.gov/catdir/toc/fy031/2002283707.html", acknowledgement = ack-nhfb, } @Proceedings{Anonymous:2003:CRN, editor = "Anonymous", booktitle = "5th Conference on Real Numbers and Computers 2003 --- RNC5, Lyon, France, September 2003", title = "5th Conference on Real Numbers and Computers 2003 --- {RNC5}, Lyon, France, September 2003", publisher = "????", address = "????", pages = "????", year = "2003", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Jun 25 14:57:33 2005", acknowledgement = ack-nhfb, } @Book{Wahdan:2004:IHE, editor = "Abdel-Moniem Wahdan", booktitle = "{ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt}", title = "{ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xlv + 954", year = "2004", bibdate = "Tue Jul 19 08:01:02 MDT 2005", bibsource = "melvyl.cdlib.org:210/CDL90", note = "IEEE catalog number 04EX893.", acknowledgement = ack-nhfb, subject = "Electric engineering; Congresses; Electronics; Congresses; Computer engineering; Congresses", } @Proceedings{IEEE:2005:PIS, editor = "{IEEE}", booktitle = "{Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA}", title = "{Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "????", year = "2005", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Tue Jun 21 19:02:16 2005", bibsource = "http://arith17.polito.it/", acknowledgement = ack-nhfb, xxnote = "Not yet published: check editor??", } @Proceedings{Anonymous:2006:PCR, editor = "Anonymous", booktitle = "{Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7) LORIA, Nancy, France, July 10--12, 2006}", title = "{Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7) LORIA, Nancy, France, July 10--12, 2006}", publisher = "????", address = "????", pages = "????", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Tue Jun 27 10:26:43 2006", bibsource = "http://rnc7.loria.fr/", acknowledgement = ack-nhfb, }