REFERENCES    

                      G. W. (Pete) Stewart

This is my bibtex reference base.  It is available by anonymous ftp
at

          thales.cs.umd.edu

in the directory

          pub/references

It is also available from netlib.  In using it, keep in mind the
following points.

SCOPE

The reference base is a combination of my personal reference
base and a number of others.  It includes (at least in part)

   1. The bibliography from Introduction to Matrix Computations
      by G. W. Stewart.

   2. The bibliography from Matrix Perturbation Theory by
      G. W. Stewart and J.-G. Sun.

   3. Ake Bjorck's bibliography on least squares.

   4. The bibliography from Matrix Computations by G. H. Golub
      and C. Van Loan.

   5. P. C. Hansen's bibliography on rank-revealing decompositions.

UPDATES

The reference base on thales will be updated from time to time, and
items can disappear.  For example, I will generally remove techreports
as I find them published in journals.  If you use this base in a
\bibliography command, save your bbl files.

CITATION KEYS

A citation key is divided into two fields <authors>:<date> separated
by a colon.  The author field is constructed as follows.  If there is
only one author, the first four letters of his or her last name are
used to form the field (but only one letter each from prefixes; e.g.
van de Geign becomes vdge).  If there are two authors the first two
letters in their last names are used.  If there are three authors the
first two letters of the first are used with one letter from each of
the second and third.  If their are four, one letter from each is
used.  Cave:  these conventions are not cast in iron.

NAMES

Names appear in the order they appear in the reference, and entries
are alphabetized by the first name to appear.  To keep bibtex from
becoming confused, only initials of given names are used.

Speaking of alphabetization, between some entries you will find
curious clusters of two letters--e.g.  -ac- -ad-.  I use them to
position myself within the reference base when I am inserting items.
I strongly recommend that you adopt some such convention if you plan
to build a large reference base.

KEYWORDS

Each entry has a keyword field, labeled kwds.  The program bibsrch
(see below) will search the file for matches in a user specified
combination of conjunctions, disjunctions, and negations.  The user
can also specify the author.  The program getkey dumps the keywords
on the standard output.  To get an alphabetized list of all key words
from the file ref.bib try

          getkey ref | sort -uf > keywords

The choice of key words is a highly personal matter, and my choices
suffer from the additional handicap that they were made on the fly as
the reference base grew.  In the matter of general subject
categories, I tend to list the most specific.  Thus, if a paper is
classified as numerical linear algebra (abbreviated nla), it is not
also classified as numerical analysis (na).  Combinations of key
words are especially tricky.  For example, the key phrase 'Lanczos
algorithm' is seldom combined with the key word 'sparse', since the
main application of the Lanczos algorithm is to sparse matrices.
Fortunately, bibsrch is flexible enough to pick out entries with
either key word, or both.

I have used a number of abbreviations to keep the kwds field to a
manageable size.  Here they are.

          cs    : computer science
          csd   : CS decomposition
          eig   : eigenvalue problems
          eriv  : errors in variables
          geig  : generalized eigenvalue problems
          ginv  : generalized inverse
          gsvd  : generalized singular value decomposition
          iter  : iterative methods
          la    : linear algebra
          lsq   : least squares
          math  : mathematics
          lud   : LU decomposition
          na    : numerical analysis
          nla   : numerical linear algebra
          nlop  : nonlinear equations and optimization
          nllsq : nonlinear least squares
          prll  : parallel computations
          pert  : perturbation theory
          qrd   : QR decomposition
          regr  : regression
          stat  : statistics
          svd   : singular value decomposition

The program getkey also prints out these correspondences in the
appropriate places.  (They are actually key words in the last article
of the base; take a look.)

DISCLAIMERS

Anyone who has had to read my papers or books knows that as a
proofreader I am at the bottom of the heap.  This reference base is
no exception.  Do not use the references in a paper, unless you have
checked them out for yourself (actually sound scholarly practice
requires that you never make an indirect reference without giving the
secondary source).  Naturally, I am interested in hearing about any
errors you may find.

BIBSRCH

The programs bibsrch and getkey may be generated from the file
bibsrch.tar, available along with this reference base.  Simply place
bibsearch.tar in the directory where you want the directory
containing the programs.  Then

          tar xf bibsearch.tar
          cd bibsearch
          more README

and you will be told what to do next.

Pete Stewart


-aa-
@article{aase:71,
   author = "J. O. Aasen",
   year = "1971",
   title = "On the Reduction of a Symmetric Matrix to Tridiagonal Form",
   journal = "BIT",
   volume = "11",
   pages = "233-242",
   kwds = "nla, symmetric matrix, tridiagonal matrix"
}

-ab-

@article{abde:71,
   author = "N. N. Abdelmalek",
   year = "1971",
   title = "Roundoff Error Analysis for {Gram-Schmidt} Method and 
	Solution of Linear Least Squares Problems, BIT {\bf 11}, 345--368.",
   journal = "BIT",
   volume = "11",
   pages = "345--368",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "rounding error ,Gram-Schmidt algorithm, qrd"
}

@article{abde:74,
   author = "N. N. Abdelmalek",
   year = "1974",
   title = "On the Solution of Least Squares Problems and Pseudo-Inverses",
   journal = "Computing",
   volume = "13",
   pages = "215--228",
   kwds = "la, pert, lsq, ginv"
}

-ac- -ad-

@inproceedings{adgs:91,
   author = "G. Adams and M. F. Griffin and G. W. Stewart",
   year = "1991",
   title = "Direction-of-Arrival Estimation Using the Rank-Revealing
             {URV}~Decomposition",
   booktitle = "Proceedings of the IEEE International Conference on
                 Acoustics, Speech and Signal Processing",
   editor = "",
   pages = "",
   publisher = "IEEE",
   address = "Washington, DC",
   note = "To appear.",
   kwds = "nla, rank determination, direction of arrival, urvd"
}

@article{ascr:84,
   author = "L. Adams and T. Crockett",
   year = "1984",
   title = "Modelling Algorithm Execution Time on Processor Arrays",
   journal = "{IEEE} Computer",
   volume = "17",
   pages = "38--43",
   note = "Cited in \cite{govl:89}.",
   kwds = "cs, prll"
}

@article{adam:85,
   author = "L. Adams",
   year = "1985",
   title = "{m}-step Preconditioned Conjugate Gradient Methods",
   journal = "{SIAM} Journal on Scientific and Statistical Computing",
   volume = "6",
   pages = "452--463",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, conjugate gradients, preconditioning"
}

-af-

@article{afri:56,
   author = "S. N. Afriat",
   year = "1956",
   title = "On the Latent Vectors and Characteristic Values of
             Products of Pairs of Symmetric Idempotents",
   journal = "Quarterly Journal of Mathematics",
   volume = "7",
   pages = "76-78",
   kwds = "la, eig, projection"
}

@article{afri:57,
   author = "S. N. Afriat",
   year = "1957",
   title = "Orthogonal and Oblique Projectors and the Characteristics of Pairs
             of Vector Spaces",
   journal = "Proceedings of the Cambridge Philosophical Society",
   volume = "53",
   pages = "800-816",
   kwds = "la, eig, projection, canonical angles"
}

-ag- -ah-

@book{ahhu:74,
   author = "A. V. Aho and J. E. Hopcroft and J. D. Ullman",
   year = "1974",
   title = "The Design and Analysis of Computer Algorithms",
   publisher = "Addison-Wesley",
   address = "Reading, Massachusetts",
   kwds = "algorithms, complexity, book"
}

-ai-

@article{aitk:34,
   author = "A. C. Aitken",
   year = "1934",
   title = "On Least Squares and Linear Combinations of Observations",
   journal = "Proceedings of the Royal Society of Edinburgh",
   volume = "55",
   pages = "42-47",
   kwds = "la, stat, lsq, regr"
}

-aj- -ak- -al-

@phdthesis{alba:84,
   author = "M. Al-Baali",
   year = "1984",
   title = "Methods for Nonlinear Least Squares",
   school = "University of Dundee",
   adress = "Department of Mathematical Sciences",
   note = "",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, lsq, nllsq"
}

@article{alfl:85,
   author = "M. Al-Baali and R. Fletcher",
   year = "1985",
   title = "Variational Methods for Non-linear Least Squares",
   journal = "J. of the Operational Research Society",
   volume = "36",
   pages = "405--421",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, lsq, nllsq"
}

@article{albfl:86,
   author = "M. Al-Baali and R. Fletcher",
   year = "1986",
   title = "An Efficient Line Search for Nonlinear Least-squares",
   journal = "J. Opt. Theory Appl.",
   volume = "48",
   pages = "359--377",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, lsq, nllsq"
}

@book{albe:72,
   author = "A. Albert",
   year = "1972",
   title = "Regression and the Moore-Penrose Pseudoinverse",
   publisher = "Academic Press",
   address = "New York",
   kwds = "book, la, stat, regr, ginv"
}

@article{alpp:88,
   author = "S. T. Alexander and C.-T. Pan and R. J. Plemmons",
   year = "1988",
   title = "Analysis of a recursive Least Squares Hyperbolic
             Rotation Algorithm for Signal Processing",
   journal = "Linear Algebra and Its Applications",
   volume = "98",
   pages = "3-40",
   kwds = "nla, lsq, updating, hyperbolic transformation, signal processing"
}

@article{allg:73,
   author = "E.L. Allgower",
   year = "1973",
   title = "Exact Inverses of Certain Band Matrices",
   journal = "Numerische Mathematik",
   volume = "21",
   pages = "279--284",
   note = "Cited in \cite{govl:89}.",
   kwds = "la, inverse matrix, band matrix"
}

@article{alma:85,
   author = "G. S. Almas",
   year = "1985",
   title = "Overview of Parallel Computing",
   journal = "Parallel Computing",
   volume = "2",
   pages = "191-203",
   kwds = "prll, architecture"
}

@article{altm:61,
   author = "N. Altman",
   year = "1961",
   title = "An Iterative Method for Eigenvalues and Eigenvectors
            of Matrices",
   journal = "Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.",
   volume = "9",
   pages = "639--644, 727--732, 751--755",
   kwds = "nla, eig, sparse"
}

@article{alva:90,
   author = "F. L. Alvarado",
   year = "1990",
   title = "Manipulating and Visualization of Sparse Matrices",
   journal = "ORSA Journal on Computing",
   volume = "2",
   pages = "186--207",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "sparse, software"
}

-am-

@article{amir:56,
   author = "A. R. Amir-Mo\'ez",
   year = "1956",
   title = "Extremal Properties of Eigenvalues of a {Hermitian}
             Transformation and the Singular Values of the Sum
             and Product of Linear Transformations",
   journal = "Duke Mathematical Journal",
   volume = "23",
   pages = "463--476",
   kwds = "la, pert, eig, symmetric matrix"
}

@article{amgr:88,
   author = "G. S. Ammar and W. B. Gragg",
   year = "1988",
   title = "Superfast Solution of Real Positive Definite
             Toeplitz Systems",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "9",
   pages = "61--76",
   kwds = "nla, fast algorithm, linear system, Toeplitz matrix"
}

@article{amgr:91,
   author = "G. S. Ammar and W. B. Gragg",
   year = "1991",
   title = "{$O(n^2)$} Reduction Algorithms for the Construction
             of a Band Matrix from Spectral Data",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "12",
   pages = "426--431",
   kwds = "nla, eig, inverse eigenvalue problem"
}

-an-

@article{ande:74,
   author = "A. H. Andersen",
   year = "1974",
   title = "Multidimensional Contigency Tables",
   journal = "Scand.\ J.\ Statist",
   volume = "1",
   pages = "115-127",
   kwds = "stat, contingency table, categorical data"
}

@book{abbd:92,
   author = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and
      J. Dongarra and J. Du Croz and A. Greenbaum and
      S. Hammarling and A. McKenney and S. Ostrouchov and
      D. Sorensen",
   year = "1992",
   title = "{LAPACK} Users' Guide, Release 1.0",
   publisher = "SIAM",
   address = "Philadelphia",
   note = "To appear.",
   kwds = "book, nla, software"
}

@article{anos:77,
   author = "D. H. Anderson and M. R. Osborne",
   year = "1977",
   title = "Discrete, Nonlinear Approximation Problems in
             Polyhedral Norms",
   journal = "Numerische Mathematik",
   volume = "28",
   pages = "157-170",
   kwds = "nlop"
}

@article{anka:75,
   author = "N. Anderson and I. Karasalo",
   year = "1975",
   title = "On Computing Bounds for the Least Singular Value of a Triangular 
	Matrix",
   journal = "BIT",
   volume = "15",
   pages = "1--4",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "pert, rank determination, svd"
}

@article{anlo:73,
   author = "P. Anderson and G. Loizou",
   year = "1973",
   title = "On the Quadratic Convergence of an Algorithm that Diagonalizes
            a Complex Symmetric Matrix",
   journal = "Journal of the Institute of Mathematics and its Applications",
   volume = "12",
   pages = "261--271",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, symmetric matrix, complex matrix, Jacobi-like"
}

@article{anlo:76,
   author = "P. Anderson and G. Loizou",
   year = "1976",
   title = "A {J}acobi-Type Method for Complex Symmetric Matrices 
            ({H}andbook)",
   journal = "Numerische Mathematik",
   volume = "25",
   pages = "347--363",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, symmetric matrix, complex matrix, Jacobi-like"
}

@article{ande:76,
   author = "T. W. Anderson",
   year = "1976",
   title = "Estimation of Linear Functional Relationships:  Approximate
             Distributions and Connections with Simultaneous Equations in
             Econometrics ",
   journal = "Journal of the Royal Statistical Society",
   volume = "38",
   pages = "1-31",
   kwds = "stat, regr, eriv, functional model"
}

@article{ande:84,
   author = "T. W. Anderson",
   year = "1984",
   title = "Estimating Linear Statistical Relationships",
   journal = "Annals of Statistics",
   volume = "12",
   pages = "1-45",
   kwds = "stat, regr, eriv, functional model"
}

@article{anou:87,
   author = "T. W. Anderson and I. Olkin and L. G. Underhill",
   year = "1987",
   title = "Generation of Random Orthogonal Matrices",
   journal = "{SIAM} Journal on Scientific and Statistical Computing",
   volume = "8",
   pages = "625--629",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, random matrix, orthogonal matrix"
}

@article{ando:89,
   author = "T. Ando",
   year =  "1989",
   title = "Majorization, Doubly Stochastic Matrices, and Comparison
            of Eigenvalues.",
   journal = "Linear Algebra and Its Applications",
   volume = "118",
   pages = "163--248",
   kwds = "la, eig, majorization, doubly stochastic matrix"
}

@techreport{ancl:91,
   author = "A. L. Andrew and K. W. E. Chu and P. Lancaster",
   year = "1991",
   title = "Derivatives of Eigenvalues and Eigenvectors
             of Matrix Functions",
   institution = "Department of Mathematics and Statistics,
                   University of Calgary",
   type = "Research Paper",
   number = "171",
   kwds = "la, pert, eig"
}

@article{ansc:83,
   author = "G. Andrews and F. B. Schneider",
   year = "1983",
   title = "Concepts and Notations for Concurrent Programming",
   journal = "{ACM} Computing Surveys",
   volume = "15",
   pages = "1--43",
   note = "Cited in \cite{govl:89}.",
   kwds = "cs, prll"
}

@article{anetal:87,
   author = "M. Annoratone and E. Arnould and T. Gross and H. T. Kung
              and O. Menzicioglu and J. A. Webb",
   year = "1987",
   title = "The WARP Computer: Architecture, Implementation,
             and Performance",
   journal = "IEEE Transaction on Computers",
   volume = "C-36",
   pages = "1523-1538",
   kwds = "prll, warp"
}

@book{ansi:76,
   author = "ANSIA",
   year = "1978",
   title = "American National Standard Programming Language FORTRAN",
   publisher = "American National Standards Institute",
   address = "New York",
   kwds = "book, fortran"
}

-ao- -ap- -aq- -ar-

@article{argg:88,
   author = "P. Arbenz and W. Gander and G. H. Golub",
   year = "1988",
   title = "Restricted Rank Modification of the Symmetric
             Eigenvalue Problem: Theoretical Considerations",
   journal = "Linear Algebra and Its Applications",
   volume = "104",
   pages = "75-96",
   kwds = "nla, eig, symmetric matrix, updating"
}

@article{argo:88,
   author = "P. Arbenz and G. H. Golub",
   year = "1988",
   title = "On the Spectral Decomposition of {H}ermitian Matrices Subject to
            Indefinite Low Rank Perturbations with Applications",
   journal = "{SIAM} Journal on Matrix Analysis and Applications",
   volume = "9",
   pages = "40--58",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, updating, symmetric matrix, indefinite matrix"
}

@article{arbe:91,
   author = "P. Arbenz",
   year = "1991",
   title = "Computing Eigenvalues of Banded Symmetric
             Toeplitz Matrices",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "12",
   pages = "743--754",
   kwds = "nla, eig, band matrix, Toeplitz matrix, circulant matrix,
            symmetric matrix"
}

@article{argo:92,
   author = "P. Arbenz and G. H. Golub",
   year = "1992",
   title = "QR-Like Algorithms for Symmetric Arrow Matrices",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "13",
   pages = "655--662",
   kwds = "nla, arrowhead matrix, QR algorithm, eig"
}

@article{arro:85,
   author = "M. Arioli and F. Romani",
   year = "1985",
   title = "Relations Between Condition Numbers and the Convergence of the
            {J}acobi Method for Real Positive Definite Matrices",
   journal = "Numerische Mathematik",
   volume = "46",
   pages = "31--42",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, condition, eig, Jacobi's method"
}

@article{arla:86,
   author = "M. Arioli and A. Laratta",
   year = "1986",
   title = "Error Analysis of an Algorithm for Solving an Underdetermined 
		Linear System",
   journal = "Numerische Mathematik",
   volume = 46,
   pages = "255--268",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, rounding error, undertermined system"
}

@article{arla:86a,
   author = "M. Arioli and A. Laratta",
   year = "1986",
   title = "Error analysis of algorithms for computing the projection of a 
	Point onto a linear manifold",
   journal = "Linear Algebra Appl.",
   volume = 82,
   pages = "1--26",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, rounding error, orthogonalization, projection"
}


@article{ardd:89,
   author = "M. Arioli and J. Demmel and I. S. Duff",
   year = "1989",
   title = "Solving Sparse Linear Systems with Sparse Backward Error",
   journal = " SIAM Journal on Matrix Analysis and Applications",
   volume = "10",
   pages = "165--190",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, sparse, pert, backward perturbation"
}

@article{ardr:89,
   author = "M. Arioli and I. S. Duff and van Rijk, P. P. M.",
   year = "1989",
   title = "On the Augmented System Approach to Sparse Least-Squares
             Problems",
   journal = "Numerische Mathematik",
   volume = "55",
   pages = "667--685",
   kwds = "nla, lsq, pert, sparse"
}

@article{ardn:92,
   author = "M. Arioli and I. S. Duff and J. Noailles and D. Ruiz",
   year = "1990",
   title = "A Block Projection Method for Sparse Matrices",
   journal = "SIAM J. Scient. Statist. Comput.",
   volume = "13",
   pages = "47--70",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, linear system, sparse, projection method"
}

@techreport{arca:76,
   author = "E. S. Armstrong and A. K. Caglayan",
   year = "1976",
   title = "An Algorithm for the Weighting Matrices in the Sample-Data Optimal
            Linear Regulator Problem",
   number = "TN D-8372",
   institution = "NASA",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, control, weighting"
}

@article{arla:84,
   author = "W. F. Arnold and A. J. Laub",
   year = "1984",
   title = "Generalized Eigenproblem Algorithms and Software for Algebraic
            {R}iccati Equations",
   journal = "Proceedings of the {IEEE}",
   volume = "72",
   pages = "1746--1754",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, geig, Riccati equation"
}

@article{arno:51,
   author = "W. E. Arnoldi",
   year = "1951",
   title = "The Principle of Minimized Iterations in the Solution of the
            Matrix Eigenvalue Problem",
   journal = "Quarterly of Applied Mathematics",
   volume = "9",
   pages = "17--29",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Arnoldi's method, eig, sparse"
}

@inproceedings{akms:85,
   author = "E. Arnould and H. T. Kung and O. Menzileioglu and
              K. Sarocky",
   year = "1985",
   title = "A Systolic Array Computer",
   booktitle = "IEEE International Conference on Acoustics, Speach,
                 and Signal Processing",
   editor = "",
   pages = "232--235",
   publisher = "IEEE",
   address = "Washington, DC",
   kwds = "cs, warp, systolic"
}

-as-

@phdthesis{ashb:87,
   author = "S. F. Ashby",
   year = "1987",
   title = "Polynomial Preconditioning for Conjugate Gradient Methods",
   school = "Computer Science Department, University of Illinois",
   address = "ILL",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, conjugate gradients, preconditioning"
}

@article{asms:90,
   author = "S. F. Ashby and T. A. Manteuffel and P. E. Saylor",
   year = "1990",
   title = "A Taxonomy for Conjugate Gradient Methods",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "27",
   pages = "1542--1568",
   kwds = "nla, conjugate gradients, linear system"
}

@incollection{ashk:71,
   author = "V. Ashkenazi",
   year = "1971",
   title = " Geodetic Normal Equations",
   booktitle = "Large Sets of Linear Equations. Ed. J.K. Reid ",
   pages = "57--74",
   publisher = "Academic Press",
   address = "New York",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, normal equations, geodesy"
}

@article{aspl:59,
   author = "E. Asplund",
   year = "1959",
   title = "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy
            {$a_{ij} = 0$, $j > i+p$}",
   journal = "Mathematica Scandinavica",
   volume = "7",
   pages = "57--60",
   note = "Cited in \cite{govl:89}.",
   kwds = "la, inverse matrix, band matrix"
}

-at- -au-

@techreport{auch:90,
   author = "G. Auchmuty",
   year = "1990",
   title = "A Posteriori Error Estimates for Linear Equations",
   institution = "Department of Mathematics, University of Houston",
   type = "Research Report",
   number = "UH/MD-91",
   kwds = "nla, pert, residual bound, linear system"
}

@article{auto:02,
   author = "L. Autonne",
   year = "1902",
   title = "Sur les groupes lin\'eaires, r\'eels et orthogonaux",
   journal = "Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France",
   volume = "30",
   pages = "121-134",
   kwds = "la, polar decomposition"
}

@article{auto:13,
   author = "L. Autonne",
   year = "1913",
   title = "Sur les matrices hypohermitiennes et les unitairs",
   journal = "Comptes Rendus de l'Academie des Sciences, Paris",
   volume = "156",
   pages = "858-860",
   kwds = "math, la, svd"
}

@article{auto:15,
   author = "L. Autonne",
   year = "1915",
   title = "Sur les matrices hypohermitiennes et sur les matrices
            unitaires",
   journal = "Annales De L'Universit\'e de Lyons, Nouvelle S\'erie I",
   volume = "38",
   pages = "1--77",
   kwds = "la, svd, polar decomposition"
}

-av-

@inproceedings{avto:79,
   author = "J. K. Avila and J.A. Tomlin",
   year = "1979",
   title = "Solution of Very Large Least Squares Problems by Nested Dissection 
	on a Parallel Processor",
   booktitle = "In Proceedings of Computer Science and Statistics:
                Twelfth Annual Symposium on the Interface", 
   publisher = "Department of Computer Science",
   address = "Waterloo, Canada",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, sparse"
}

-aw- -ax-

@incollection{axel:77,
   author = "O. Axelsson",
   year = "1977",
   title = "Solution of Linear Systems of Equations: Iterative Methods",
   booktitle = "Sparse Matrix Techniques: {C}openhagen, 1976",
   editor = "V. A. Barker",
   publisher = "Springer-Verlag",
   address = "Berlin",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, linear system, iter, sparse"
}

@article{axel:80,
   author = "O. Axelsson",
   year = "1980",
   title = "Conjugate Gradient Type Methods for Unsymmetric and Inconsistent
            Systems of Linear Equations",
   journal = "Linear Algebra and its Applications",
   volume = "29",
   pages = "1--66",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, linear system, conjugate gradients, nonsymmetric matrix"
}

@article{axel:85,
   author = "O. Axelsson",
   year = "1985",
   title = "A Survey of Preconditioned Iterative Methods for Linear Systems of
            Equations",
   journal = "{BIT}",
   volume = "25",
   pages = "166--187",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, linear system, sparse, iter, preconditioning,
           conjugate gradients"
}

@article{axpo:86,
   author = "O. Axelsson and B. Polman",
   year = "1986",
   title = "On Approximate Factorization Methods for Block Matrices Suitable
            for Vector and Parallel Processors",
   journal = "Linear Algebra and Its Applications",
   volume = "77",
   pages = "3--26",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, block matrix, prll"
}

-ay- -az-
-ba-

@incollection{baos:91,
   author = "I. Babu\v{s}ka and J. Osborn",
   year = "1991",
   title = "Eigenvalue Problems",
   booktitle = "Handbook of Numerical Analysis, Vol.~II.",
   editor = "P. G. Ciarlet and J. L. Lions",
   pages = "643--787",
   publisher = "Elsevier",
   address = "New York",
   kwds = "na, eig, functional analysis, pert"
}

@article{bai:88,
   author = "Z. Bai",
   year = "1988",
   title = "Note on the Quadratic Convergence of {Kogbetliantz's}
             Algorithm for Computing the Singular Value Decomposition",
   journal = "Linear Algebra and Its Applications",
   volume = "104",
   pages = "131-140",
   kwds = "nla, Kogbetliantz's algorithm, svd, Jacobi-like"
}

@unpublished{badm:89,
   author = "Z. Bai and J. Demmel and A. Mckenney",
   year = "1989",
   title = "On the Conditioning of the Nonsymmetric Eigenproblem:
             Theory and Software",
   note = "LAPACK Working Note",
   kwds = "nla, eig, pert, nonsymmetric matrix, condition"
}

@unpublished{bade:92,
   author = "Z. Bai and J. W. Demmel",
   year = "1991",
   title = "On a Direct Algorithm for Computing Invariant Subspaces
            with Specified Eigenvalues",
   note = "Department of Mathematics, University of Kentucky (first
           author).  Manuscript submitted to {\it Linear Algebra
           and Its Applications.\/}",
   kwds = "nla, eig, Schur form"
}

@article{bail:88,
   author = "D. Bailey",
   year = "1988",
   title = "Extra High Speed Matrix Multiplication on the {C}ray-2",
   journal = "{SIAM} Journal on Scientific and Statistical Computing",
   volume = "9",
   pages = "603--607",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, vect, matrix multiplication"
}

@article{bana:22,
   author = "S. Banach",
   year = "1922",
   title = "Sur les op\'erations dans les ensembles abstraits
             et leur application aux \'equations integrales",
   journal = "Fundamenta Mathematicae",
   volume = "3",
   pages = "133--181",
   kwds = "norm, Banach space, functional analysis"
}

@article{bana:29,
   author = "S. Banach",
   year = "1929",
   title = "Sur les functionnelles lin\'eaires {II}.",
   journal = "Studia Mathematica",
   volume = "1",
   pages = "223-239",
   kwds = "Hahn-Banach theorem, functional analysis"
}

@book{bana:32,
   author = "S. Banach",
   year = "1932",
   title = " {Th\'eorie Op\'erations Lin\'eaires}",
   publisher = "Hafner Publishing Co.",
   address = "New York",
   kwds = "book, Banach space, Hahn-Banach theorem, functional analysis"
}

@article{baro:77,
   author = "R. E. Bank",
   year = "1977",
   title = "Marching Algorithms for Elliptic Boundary Value Problems.
             {I}:  The Constant Coefficient Case",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "14",
   pages = "950-970",
   kwds = "pde, elliptic pde"
}

@article{bank:77,
   author = "R. E. Bank",
   year = "1977",
   title = "Marching Algorithms for Elliptic Boundary Value Problems.
             {II}:  The Variable Coefficient Case",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "14",
   pages = "950-970",
   kwds = "pde, elliptic pde"
}

@book{bard:74,
   author = "Y. Bard",
   year = "1974",
   title = "Nonlinear Parameter Estimation",
   publisher = "Academic Press",
   address = "New York",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "book, stat, nlop, lsq, nllsq"
}

@techreport{bare:82,
   author = "E. H. Bareiss",
   year = "1982",
   title = "Numerical Solution of the Weighted Linear Least Squares Problems 
	by {G}-transformations",
   institution = "Department of Electrical Engineering and Computer Science",
   adress = "Northwestern University, Evanston, Illinois",
   type = "Technical Report",
   number = "82-03-NAM-03, April 1982",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, weights"
}

@techreport{bamv:47,
   author = "V. Bargmann and D. Mongomery and von Neumann, J.",
   year = "1947",
   title = "Solutions of Linear Systems of High Order",
   institution = "Navy Bu. Ord.",
   type = "Report",
   number = "",
   note = "In \cite[V.~4, 421--478]{vneu:62}.",
   kwds = "nla, rounding error, linear system"
}


@article{bari:75,
   author = "I. Y. Bar-Itzhack",
   year = "1975",
   title = "Iterative Optimal Orthogonalization of the Strapdown Matrix",
   journal = "{IEEE} Transactions on Aerospace and Electronic Systems",
   volume = "11",
   pages = "30--37",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, iter, orthogonalization"
}

@unpublished{bapl:,
   author = "G. P. Barker and R. J. Plemmons",
   year = "1984?",
   title = "Convergence of {Gauss-Seidel} Iterations for Computing
             Stationary Distributions of {Markov} Chains",
   note = "Manuscript, North Carolina State University",
   kwds = "nla, Markov chain, Gauss-Seidel iteration, iter, relaxation"
}

@article{barl:85,
   author = "J. L. Barlow",
   year = "1985",
   title = "Stability Analysis of the {G}-algorithm and a
            Note on its Application to Sparse Least Squares Problems",
   journal = "BIT",
   volume = "25",
   pages = "507--520",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, weights, sparse"
}

@article{baba:85,
   author = "J. L. Barlow and E. H. Bareiss",
   year = "1985",
   title = "On Roundoff Error Distributions in Floating Point
             and Logarithmic Arithmetic",
   journal = "Computing",
   volume = "24",
   pages = "325--347",
   kwds = "rounding error, stochastic analysis, computer arithmetic"
}

@article{baba:85a,
   author = "J. L. Barlow and E. H. Bareiss",
   year = "1985",
   title = "Probabilistic Error Analysis of Gaussian Elimination
              in Floating Point and Logarithmic Arithmetic",
   journal = "Computing",
   volume = "34",
   pages = "349--364",
   kwds = "nla, lud, rounding error, stochastic analysis, computer arithmetic"
}

@article{barl:86,
   author = "J. L. Barlow",
   year = "1986",
   title = "On the Smallest Positive Singular Value of a Singular
             {$M$}-Matrix with Applications to Ergodic {Markov} Chains",
   journal = "SIAM Journal on Algebraic and Discrete Methods",
   volume = "7",
   pages = "414--424",
   kwds = "nla, Markov chain, M-matrix, svd, singular system"
}

@article{baip:87,
   author = "J. L. Barlow and I. C. F. Ipsen",
   year = "1987",
   title = "Scaled {Givens} Rotations for the Solution of Linear
            Least Squares Problems on Systolic Arrays",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "8",
   pages = "716-734",
   kwds = "nla, prll, qrd, lsq, systolic, plane rotation"
}

@article{barl:88,
   author = "J. L. Barlow",
   year = "1988",
   title = "Error Analysis and Implementation Aspects of Deferred Correction 
	for Equality Constrained Least Squares Problems",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "25",
   pages = "1340--1358",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, rounding error, constraints"
}

@techreport{bade:88,
   author = "J. Barlow and J. Demmel",
   year = "1988",
   title = "Computing Accurate Eigensystems of Scaled Diagonally
             Dominant Matrices",
   institution = "Computer Science Department, Courant Institute",
   type = "Technical Report",
   number = "421",
   note = "Cited in \cite{deve:89}.  To appear in {\it SIAM Journal
            on Numerical Analysis\/}",
   kwds = "la, nla, pert, eig, diagonal dominance"
}

@article{baha:88,
   author = "J. L. Barlow and S. L. Handy",
   year = "1988",
   title = "The Direct Solution of Weighted and Equality
             Constrained Least-Squares Problems",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "9",
   pages = "704-716",
   kwds = "nla, lsq, constraints, weights"
}

@article{banp:88,
   author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
   year = "1988",
   title = " Iterative Methods for Equality-constrained Least Squares 
	Problems.",
   journal = "SIAM Journal on Scientific and  Statistical Computing",
   volume = "9",
   pages = "892--906",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, iter, constraints"
}

@techreport{barl:90,
   author = "J. L. Barlow",
   year = "1990",
   title = "Error Analysis of a Pairwise Summation Algorithm
             to Compute the Sample Variance",
   institution = "Department of Computer Science, Pennsylvania State
                   University",
   type = "Technical Report",
   number = "CS-90-10",
   kwds = "stat, variance, standard deviation"
}

@techreport{barl:91,
   author = "J. L. Barlow",
   year = "1991",
   title = "Error Analysis of Update Methods for the Symmetric
             Eigenvalue Problem",
   institution = "Department of Computer Science, Pennsylvania
                   State University",
   type = "Technical Report",
   number = "CS-91-09",
   kwds = "nla, prll, eig, symmetric matrix, update"
}

@techreport{barl:91a,
   author = "J. L. Barlow",
   year = "1991",
   title = "Error Bounds and Condition Estimates for the Computation
             of Null Vectors with Applications to {Markov} Chains",
   institution = "Department of Computer Science, Pennsylvania
                   State University",
   type = "Technical Report",
   number = "CS-91-20",
   kwds = "la, nla, eig, condition estimation, Markov chain"
}

@techreport{bave:91,
   author = "J. L. Barlow and U. B. Vemulapati",
   year = "1991",
   title = "Rank Detection Methods for Sparse Matrices",
   institution = "Department of Computer Science, Pennsylvania
                   State University",
   type = "Technical Report",
   number = "CS-91-21",
   kwds = "nla, condition estimation, rank determination"
}

@article{bast:68,
   author = "S. Barnett and C. Storey",
   year = "1968",
   title = "Some Applications of the {L}yapunov Matrix Equation",
   journal = "Journal of the Institute of Mathematics and its Applications",
   volume = "4",
   pages = "33--42",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Lyapunov equation, matrix equation"
}

@techreport{barr:88,
   author = "Anders Barrlund",
   year = "1988",
   title = "Perturbation Bounds on the Polar Decomposition",
   institution = "Institute of Information Processing, University
                   of Ume{\aa}",
   type = "Report",
   number = "UMINF-146.88",
   kwds = "la, pert, polar decomposition"
}

@article{barr:91,
   author = "A. Barrland",
   year = "1991",
   title = "Perturbation Bounds for the {$LDL^{\rm H}$} and
            the {$LU$}~factorizations",
   journal = "BIT",
   volume = "31",
   pages = "358--363",
   kwds = "la, pert, lud"
}

@article{baro:73,
   author = "I. Barrodale and F. D. K. Roberts",
   year = "1973",
   title = "An Improved Algorithm for Discrete $\ell_1$ Linear Approximation",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "10",
   pages = "839--848",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, l1 approximation"
}

@article{baph:75,
   author = "I. Barrodale and C. Phillips",
   year = "1975",
   title = "Algorithm 495: Solution of an Overdetermined System of 
	Linear Equations in the Chebychev Norm ",
   journal = "ACM Transactions on Mathematical Software",
   volume = "1",
   pages = "264--270",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, Chebyshev approximation"
}

@article{bast:77,
   author = "I. Barrodale and G. F. Stuart",
   year = "1977",
   title = "A New Variant of {Gaussian} Elimination",
   journal = "Journal Inst.\ Maths.\ Applics.",
   volume = "19",
   pages = "39-47",
   kwds = "nla, lud"
}

@article{baro:78,
   author = "I. Barrodale and F. D. K. Roberts",
   year = "1978",
   title = "An Efficient Algorithm for Discrete $\ell_1$ Linear Approximation 
	with Linear Constraints",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "15",
   pages = "603--611",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, l1 approximation"
}

@article{bgkv:80,
   author = "H. Bart and I. Gohberg and M. A. Kaashoek and Van Dooren, P.",
   year = "1980",
   title = "Factorization of Transfer Functions",
   journal = "SIAM Journal on Control and Optimization",
   volume = "18",
   pages = "675--696",
   kwds = "la, transfer function"
}

@article{bago:69,
   author = "R. H. Bartels and G. H. Golub",
   year = "1969",
   title = "The Simplex Method of Linear Programming Using {LU}~Decomposition",
   journal = "Communications of the ACM",
   volume = "12",
   pages = "266-268",
   kwds = "nla, nlop, lud, linear programming, updating"
}

@incollection{bags:70,
   author = "R. H. Bartels and G. H. Golub and M. A. Saunders",
   year = "1970",
   title = "Numerical Techniques in Mathematical Programming",
   pages = "123--176",
   booktitle = "Nonlinear programming", 
   editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter",
   publisher = "Academic Press, New York",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, qrd, rank determination"
}

@article{bart:71,
   author = "R. H. Bartels",
   year = "1971",
   title = "A Stablization of the Simplex Method",
   journal = "Numerische Mathematik",
   volume = "16",
   pages = "414--434",
   kwds = "nlop, simplex method, updating"
}

@incollection{basz:71,
   author = "R. H. Bartels and J. Stoer and C. Zenger",
   year = "1971",
   title = "A Realization of the Simplex Method Based on
             Triangular Decomposition",
   booktitle = "Linear Algebra",
   editor = "J. H. Wilkinson and C. Reinsch",
   pages = "152--190",
   publisher = "Springer",
   address = "New York",
   kwds = "nla, linear programming, simplex method, lud, updating"
}

@article{bast:72,
   author = "R. H. Bartels and G. W. Stewart",
   year = " 1972",
   title = "Algorithm 432: The Solution of the Matrix
             Equation {$AX - BX = C$}",
   journal = "Communications of the ACM",
   volume = "8",
   pages = "820-826",
   kwds = "nla, Schur form, Sylvester equation, Lyapunov equation,
           matrix equation"
}

@article{bacs:78,
   author = "R. H. Bartels and A. R. Conn and J. W. Sinclair",
   year = "1978",
   title = "Minimization Techniques for Piecewise Differentiable Functions:
            The {$L_{1}$} Solution to an Overdetermined Linear System",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "15",
   pages = "224--241",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, l1 approximation, overdetermined system"
}

@article{bacc:78,
   author = "R. H. Bartels and A. R. Conn and C. Charalambous",
   year = "1978",
   title = "On {C}line's Direct Method for Solving Overdetermined
            Linear Systems in the {$L_{\infty}$} Sense",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "15",
   pages = "255--270",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Chebyshev approximation, overdetermined system"
}

@article{baco:80,
   author = "R. H. Bartels and A. R. Conn",
   year = "1980",
   title = "Linearly Constrained Discrete $\ell_1$ Problems",
   journal = "ACM Transactions on Mathematical Software",
   volume = "6",
   pages = "594--608",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, l1 approximation, software"
}

@article{bacc:80,
   author = "R. H. Bartels and A. R. Conn and C. Charalambous",
   year = "1980",
   title = "On {Cline's} Direct Method for Solving Overdetermined
            Linear Systems in the {$\ell_\infty$} Sense",
   journal = " SIAM Journal on Numerical Analysis",
   volume = "15",
   pages = "255--270",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, Chebyshev approximation"
}

@article{bacs:78,
   author = "R. H. Bartels and A. R. Conn  and J. W. Sinclair",
   year = "1978",
   title = "Minimization Techniques for Piecewise Differentiable Functions: 
	The $\ell_1$ Solution to an Overdetermined Linear System",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "15",
   pages = "224--241",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, l1 approximation"
}

@article{bamw:67,
   author = "W. Barth, R. S. Martin and J. H. Wilkinson",
   year = "1967",
   title = "Calculation of the Eigenvalues of a Symmetric
             Tridiagonal matrix by the Method of Bisection",
   journal = "Numerische Mathematik",
   volume = "9",
   pages = "386--393",
   note = "Also in \cite[pp.249--256]{wire:71}.",
   kwds = "nla, eig, symmetric matrix, tridiagonal matrix, software"
}

@article{bart:54,
   author = "Helmut Bartsch",
   year = "1954",
   title = " {Absch\"atzungen f\"ur die kleinste charakteristische
             Zahl einer positiv-definiten hermiteschen Matrix}",
   journal = "{Zeitschrift f\"ur angewandte Mathematik und Mechanik}",
   volume = "34",
   pages = "72-74",
   kwds = "la, pert, eig, symmetric matrix"
}

@article{bage:76,
   author = "V. Barwell and J. A. George",
   year = "1976",
   title = "A Comparison of Algorithms for Solving Symmetric Indefinite
            Systems of Linear Equations",
   journal = "{ACM} Transactions on Mathematical Software",
   volume = "2",
   pages = "242--251",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, linear system, symmetric matrix, indefinite system"
}

@article{bate:08,
   author = "H. Bateman",
   year = "1908",
   title = "A Formula for the Solving Function of a Certain
             Integral Equation of the Second Kind",
   journal = "Transactions of the Cambridge Philosophical Society",
   volume = "20",
   pages = "179-187",
   kwds = "na, la, svd, integral equation"
}

@article{bate:08a,
   author = "H. Bateman",
   year = "1908",
   title = "The Reality of the Roots of Certain Transcendental
             Equations Occurring in the Theory of Integral
             Equations",
   journal = "Transactions of the Cambridge Philosophical Society",
   volume = "20",
   pages = "371--381",
   kwds = "na, la, svd, integral equation"
}

@article{bate:08b,
   author = "H. Bateman",
   year = "1908",
   title = "On the Application of Integral Equations to the Determination
             of Upper and Lower Limits of a Double Integral",
   journal = "Transactions of the Cambridge Philosophical Society",
   volume = "21",
   pages = "123--128",
   kwds = "na, la, svd, integral equation"
}

@article{bate:22,
   author = "H. Bateman",
   year = "1922",
   title = "On the Numerical Solution of Linear Integral Equations",
   journal = "Proceedings of the Royal Society of London, Series A",
   volume = "100",
   pages = "441--449",
   kwds = "na, la, svd, integral equation"
}

@techreport{bawo:82,
   author = "D. M Bates and D. A. Wolf",
   year = "1982",
   title = "Non-negative Regression by Givens Rotations",
   institution = "Department of Statistics,
                   University of Wisconsin",
   number = "687",
   kwds = "stat, nla, regr, plane rotation"
}

@article{bawi:72,
   author = "K.-J. Bathe and E. L. Wilson",
   year = "1972",
   title = "Large Eigenvalue Problems in Dynamic Analysis",
   journal = "ASCE J., Eng. Mech. Div.",
   volume = "98",
   pages = "1471--1485",
   kwds = "nla, eig, sparse"
}

@article{bawi:73,
   author = "K.-J. Bathe and E. L. Wilson",
   year = "1973",
   title = "Solution Methods for Eigenvalue Problems in
             Structural Mechanics",
   journal = "International Journal for Numerical Methods in Engineering",
   volume = "6",
   pages = "213-266",
   kwds = "nla, eig, sparse"
}

@article{bawi:73a,
   author = "K.-J. Bathe and E. L. Wilson",
   year = "1973",
   title = "Eigensolution of Large Structural Systems with
            Small Bandwidth",
   journal = "ASCE J., Eng. Mech. Div.",
   volume = "99",
   pages = "467--480",
   kwds = "nla, eig, sparse"
}

@article{baue:54,
   author = "F. L. Bauer",
   year = "1954",
   title = " {Beitr\"age zur Entwicklung numerischer Verfahren
             f\"ur programmgesteuerte Rechenanlagen I. Quadratisch 
             konvergente Durchf\"uhrung der Bernoulli-Jacobischen
             Methode zur Nullstellenbestimmung von Polynomen}",
   journal = "Bayer.\ Akad.\ Wiss.\ Math.-Natur.\ Kl.\ S.-B.",
   pages = "275--303",
   kwds = "nlop, polynomial, Bernoulli's method"
}

@article{baue:56,
   author = "F. L. Bauer",
   year = "1956",
   title = " {Beitr\"age zur Entwicklung numerischer Verfahren
             f\"ur programmgesteuerte Rechenanlagen II. Direkte
             Faktorisierung eines Polynoms}",
   journal = "Bayer.\ Akad.\ Wiss.\ Math.-Natur.\ Kl.\ S.-B.",
   pages = "163--203",
   kwds = "nlop, polynomial"
}

@article{baue:56a,
   author = "F. L. Bauer",
   year = "1956",
   title = " {Das Verfahren der abgek\"urzten Iteration f\"ur algebraische
             Eigenwertprobleme, insbesondere zur Nullstellenbestimmung
             eines Polynoms}",
   journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
   volume = "7",
   pages = "17-32",
   kwds = "nla, nlop, polynomial, eig"
}

@article{baue:57,
   author = "F. L. Bauer",
   year = "1957",
   title = "{Das Verfahren der Treppeniteration und verwandte
              Verfahren zur L\"osung algebraischer Eigenwertprobleme}",
   journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
   volume = "8",
   pages = "214--235",
   kwds = "nla, eig, subspace iteration, Treppeniteration, sparse"
}

@article{basa:57,
   author = "F. L. Bauer and Klaus Samelson",
   year = "1957",
   title = "Polynomkerne und Iterationsverfahren",
   journal = "Math.\ Z.",
   volume = "67",
   pages = "93-98",
   kwds = "nla, linear system, iter"
}

@article{baue:58,
   author = "F. L. Bauer",
   year = "1958",
   title = "On Modern Matrix Iteration Processes of {Bernoulli}
             and {Graeffe} Type",
   journal = "Journal of the ACM",
   volume = "5",
   pages = "246-257",
   kwds = "nla, nlop, polynomial, Bernoulli's method, Graeffe's method"
}

@article{baue:59,
   author = "F. L. Bauer",
   year = "1959",
   title = "Sequential Reduction to Tridiagonal Form",
   journal = "SIAM Journal",
   volume = "7",
   pages = "107--113",
   kwds = "nla, eig, tridiagonal matrix"
}

@article{bafi:60,
   author = "F. L. Bauer and C. T. Fike",
   year = "1960",
   title = "Norms and Exclusion Theorems",
   journal = "Numerische Mathematik",
   volume = "2",
   pages = "137--141",
   kwds = "la, eig, norm, pert"
}

@article{baho:60,
   author = "F. L. Bauer and A. S. Householder",
   year = "1960",
   title = "Moments and Characteristic Roots",
   journal = "Numerische Mathematik",
   volume = "2",
   pages = "42--43",
   kwds = "la, eig, pert"
}

@article{baue:62,
   author = "F. L. Bauer",
   year = "1962",
   title = "On the Field of Values Subordinate to a Norm",
   journal = "Numerische Mathematik",
   volume = "4",
   pages = "103-113",
   kwds = "la, field of values, norm"
}

@article{baue:63,
   author = "F. L. Bauer",
   year = "1963",
   title = "Optimally Scaled Matrices",
   journal = "Numerische Mathematik",
   volume = "5",
   pages = "73--87",
   kwds = "nla, scaling"
}

@article{baue:65,
   author = "F. L. Bauer",
   year = "1965",
   title = "Elimination with Weighted Row Combinations for Solving
            Linear Equations and Least Squares Problems",
   journal = "Numerische Mathematik",
   volume = "7",
   pages = "338-352",
   note = "Also in \cite[pp.119--133]{wire:71}.",
   kwds = "nla, lsq, Gram-Schmidt algorithm, software"
}

@article{baue:66,
   author = "F. L. Bauer",
   year = "1966",
   title = " {Genauigkeitsfragen bei der L\"osung linear
               Gleich\-ungs\-systeme}",
   journal = "{Zeitschrift f\"ur angewandte Mathematik und Mechanik}",
   volume = "46",
   pages = "409--421",
   kwds = "la, pert, condition, scaling"
}

@article{baue:66a,
   author = "F. L. Bauer",
   year = "1966",
   title = "Inclusion Sets for Roots of Polynomials",
   journal = "Numerische Mathematik",
   volume = "9",
   pages = "173-176",
   kwds = "nlop, pert, polynomial"
}

@techreport{baue:67,
   author = "F. L. Bauer",
   year = "1967",
   title = "Theory of Norms",
   institution = "Computer Science Department School of Humanities and 
                   Sciences, Stanford University",
   type = "Technical Report",
   number = "CS 75",
   kwds = "la, norm"
}

@article{bare:68,
   author = "F. L. Bauer and C. Reinsch",
   year = "1968",
   title = "Rational {QR} Transformation with {N}ewton Shift for Symmetric
            Tridiagonal Matrices",
   journal = "Numerische Mathematik",
   volume = "11",
   pages = "264--272",
   note = "Also in \cite[pages 257--265]{WilR71}",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, QR algorithm, tridiagonal matrix"
}

@article{bads:69,
   author = "F. L. Bauer and E. Deutsch and J. Stoer",
   year = "1969",
   title = " {Absch\"atzungen F\"ur die Eigenwerte positiver linearer
             Operatoren}",
   journal = "Linear Algebra and Its Applications",
   volume = "2",
   pages = "275-301",
   kwds = "la, pert, eig"
}

@incollection{bare:70,
   author = "F. L. Bauer and C. Reinsch",
   year = "1970",
   title = "Inversion of Positive Definite Matrices by the {G}auss-{J}ordan
            Methods",
   booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra",
   editor = "J. H. Wilkinson and C. Reinsch",
   publisher = "Springer-Verlag",
   address = "New York",
   pages = "45--49",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, inverse matrix, Gauss-Jordan method"
}

@book{baum:72,
   author = "H. Baumg{\"a}rtel",
   year = "1972",
   title = " {Endlich\-dimensionale Analytische St\"orungs\-theorie}",
   publisher = "Akademie-Verlag",
   address = "Berlin",
   note = "Cited in \cite{bhat:87}.",
   kwds = "book, la, pert, eig"
}

@article{bast:79,
   author = "C. Bavely and G. W. Stewart",
   year = "1979",
   title = "An Algorithm for Computing Reducing Subspaces
             by Block Diagonalization",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "16",
   pages = "359-367",
   kwds = "nla, eig, invariant subspace, nonsymmetric matrix"
}

@article{bawi:70,
   author = "R. Bayer and C. Witzgall",
   year = "1970",
   title = "Some Complete Calculi for Matrices",
   journal = "Communications of the ACM",
   volume = "13",
   pages = "223--237",
   kwds = "la, cs"
}

-bb- -bc- -bd- -be-

@techreport{beat:64,
   author = "A. E. Beaton",
   year = "1964",
   title = "The use of Special Matrix Operators in Statistical Calculus",
   institution = "Educational Testing Service,
                   Princeton, New Jersey",
   type = "Research Bulletin",
   number = "64-51",
   kwds = "stat, nla, sweep operator, updating, inverse matrix"
}


@article{berb:76,
   author = "A. E. Beaton and D. B. Rubin and J. L. Barone",
   year = "1976",
   title = "The Acceptability of Regression Solutions:  Another Look at 
             Computational Accuracy",
   journal = "Journal of the American Statistical Association",
   volume = "71",
   pages = "158-168",
   kwds = "stat, regr, pert, eriv, rounding error, diagnostic"
}

@article{beco:83,
   author = "R. J. Bechman and R. D. Cook",
   year = "1983",
   title = "Outlier..........s",
   journal = "Technometrics",
   volume = "25",
   pages = "119-149",
   kwds = "stat, regr, diagnostic, outlier"
}

@book{bebe:71,
   author = "E. F. Beckenbach and R. Bellman",
   year = "1971",
   title = "Inequalities",
   publisher = "Springer",
   address = "New York",
   kwds = "book, na, la, inequalities, pert"
}

@article{bevd:88,
   author = "Th. Beelen and Van Dooren, P.",
   year = "1988",
   title = "An Improved Algorithm for the Computation of {Kronecker's}
             Canonical Form of a Singular Pencil",
   journal = "Linear Algebra and Its Applications",
   volume = "105",
   pages = "9-66",
   kwds = "la, nla, eig, geig, matrix pencil, Kronecker form"
}

@techreport{bdgm:91,
   author = "A. Beguelin and J. J. Dongarra and A. Geist and
              R. Mancheck and V. Sunderam",
   year = "1991",
   title = "A Users' Guide to PVM (Parallel Virtual Machine)",
   institution = "Oak Ridge National Laboratory",
   type = "Technical Report",
   number = "ORNL/TM-11826",
   kwds = "prll, operating system"
}

@book{bell:70,
   author = "R. Bellman",
   year = "1970",
   title = "Introduction to Matrix Analysis",
   publisher = "Mc Graw-Hill",
   address = "New York",
   kwds = "book, la"
}

@book{bekw:80,
   author = "D. A. Belsley and A. E. Kuh and R. E. Welsch",
   year = "1980",
   title = "Regression Diagnostics:  Identifying Influential Data and Sources
             of Collinearity",
   publisher = "John Wiley and Sons",
   address = "New York",
   kwds = "book, stat, regr, diagnostic, eriv, outlier, collinearity"
}

@article{bels:82,
   author = "D. A. Belsley",
   year = "1982",
   title = "Assessing the Presence of Harmful Collinearity and Other
             Forms of Weak Data Through a Test for Signal-to-Noise",
   journal = "Journal of Econometrics",
   volume = "20",
   pages = "211--253",
   kwds = "stat, regr, eriv, collinearity, diagnostic"
}

@article{bels:84,
   author = "D. A. Belsley",
   year = "1984",
   title = "Demeaning Conditioning Diagnostics Through Centering",
   journal = "The American Statistician",
   volume = "38",
   pages = "73-77",
   kwds = "stat, regr, diagnostic, eriv, centering"
}

@article{belt:1873,
   author = "E. Beltrami",
   year = "1873",
   title = "Sulle Funzioni Bilineari",
   journal = "Giornale di Matematiche ad Uso degli Studenti Delle Universita",
   volume = "11",
   pages = "98-106",
   note = "An English translation by D. Boley is available as University
           of Minnesota, Department of Computer Science, Technical
           Report 90--37, 1990.",
   kwds = "la, svd, history"
}

@article{besk:70,
   author = "C. F. Bender and I. Shavitt",
   year = "1970",
   title = "An Iterative Procedure for the Calculation of the Lowest
            Real Eigenvalue and Eigenvector of a Nonsymmetric Matrix",
   journal = "J. Comput. Phys.",
   volume = "6",
   pages = "146--149",
   kwds = "nla, eig, sparse, nonsymmetric matrix"
}

@article{bend:02,
   author = "I. Bendixson",
   year = "1902",
   title = "Sur les racines d'une equation fondemental",
   journal = "Acta Mathematica",
   volume = "3",
   pages = "359-366",
   kwds = "la, Bendixson's theorem"
}

@article{beni:66,
   author = "A. Ben-Israel",
   year = "1966",
   title = "On Error Bounds for Generalized Inverses",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "3",
   pages = "585--592",
   kwds = "la, pert, ginv"
}

@book{begr:73,
   author = "A. Ben-Israel and T. N. E. Greville",
   year = "1973",
   title = "Generalized Inverses:  Theory and Applications",
   publisher = "John Wiley and Sons",
   address = "New York",
   kwds = "book, la, ginv"
}

@article{bebc:88,
   author = "M. Bennani and M. C. Brunet and F. Chatelin",
   year = "1988",
   title = "De l'utilisation en calcul matriciel de mod\`eles
             probabilistes pour la simulation des erreurs de calcul",
   journal = "Comptes Rendus de l'Acad\'emie des Sciences Paris, S\'erie I",
   volume = "307",
   pages = "847--850",
   kwds = "nla, pert, rounding error, stochastic analysis"
}

@article{beno:24,
   author = "Commandant Beno{\^\i}t",
   year = "1924",
   title = "Note sur une m\'ethode de r\'esolution des \'equations
             normales provenant de l'application de la m\'ethode des
             moindres c\'arres a un syst\`em d'\'equations lin\'eares
             en nombre inf\'erieur \`a celui des inconnues. --- Application
             de la m\'ethode \`a la r\'esolution d'un syst\`eme
             d\'eini d'\'equations lin\'eares ({Proc\'ed\'e du
             Commandant Cholesky})",
   journal = "Bull\'etin G\'eod\'esique (Toulouse)",
   volume = "2",
   pages = "5--77",
   kwds = "nla, Cholesky decomposition, lud"
}

@techreport{begr:66,
   author = "J. M. Bennett and D. R. Green",
   year = "1966",
   title = "Updating the Inverse or Triangular Factors of a Modified
             Matrix",
   institution = "Computing Department, Univerisity of Sidney",
   number = "42",
   kwds = "nla, updating, inverse matrix, lud"
}

@article{bpsz:50,
   author = "P. G. Bergman and R. Penfield and R. Schiller and H. Zatkis",
   year = "1950",
   title = "The {Hamiltonian} of the General Theory of Relativity
             with Electromagnetic Field",
   journal = "Physical Review",
   volume = "52",
   pages = "1950",
   kwds = "la, ginv"
}

@inproceedings{berk:76,
   author = "K. N. Berk",
   year = "1976",
   title = "Tolerance and Condition in Regression Computations",
   booktitle = "In Proceedings of the Ninth
                 Interface Symposium on Computer
                 Science and Statistics",
   publisher = "Prindle, Weber, and Schmidt",
   address = "Boston",
   kwds = "stat, regr, condition, rank determination"
}

@article{berk:77,
   author = "K. N. Berk",
   year = "1977",
   title = "Tolerance and Condition in Regression Computations",
   journal = "Journal of the American Statistical Association",
   volume = "72",
   pages = "863--866",
   kwds = "stat, regr, condition, rank determination"
}

@article{berk:78,
   author = "K. N. Berk",
   year = "1978",
   title = "Comparing Subset Regression Procedures",
   journal = "Technometrics",
   volume = "20",
   pages = "1--6",
   kwds = "stat, regr, variable selection"
}

@article{berk:63,
   author = "E. Berkson",
   year = "1963",
   title = "Some Metrics on the Subspaces of a Banach Space",
   journal = "Pacific Journal of Mathematics",
   volume = "13",
   pages = "7--22",
   kwds = "la, subspace metric, functional analysis"
}

@article{berk:50,
   author = "J. Berkson",
   year = "1950",
   title = "Are There Two Regressions",
   journal = "Journal of the American Statistical Association",
   volume = "45",
   pages = "164-180",
   kwds = "stat, regr, eriv"
}

@article{bebe:71,
   author = "A. Berman and A. Ben-Israel",
   year = "1971",
   title = "A Note on Pencils of {H}ermitian of Symmetric Matrices",
   journal = "{SIAM} Journal on Applied Mathematics",
   volume = "21",
   pages = "51--54",
   note = "Cited in \cite{govl:89}.",
   kwds = "la, geig, symmetric matrix"
}

@article{beve:68,
   author = "M. J. M. Bernal and J. H. Verner",
   year = "1968",
   title = "On Generalizations of the Theory of Consistent Orderings for
            Successive Over-Relaxation Methods",
   journal = "Numerische Mathematik",
   volume = "12",
   pages = "215--222",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, linear system, relaxation, iter"
}

@inproceedings{besa:86,
   author = "M. Berry and A. Sameh",
   year = "1986",
   title = "Multiprocessor {J}acobi Algorithms for Dense Symmetric Eigenvalue
            and Singular Value Decompositions",
   booktitle = "Proceedings International Conference on Parallel Processing",
   pages = "433--440",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Jacobi's method, Jacobi-like, eig, svd"
}

@article{bego:91,
   author = "M. Berry and G. H. Golub",
   year = "1991",
   title = "Estimating the Largest Singular Values of Large Sparse
            Matrices via Modified Moments",
   journal = "Numerical Algorithms",
   volume = "1",
   pages = "363--374",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, sparse, svd"
}

@article{bert:1855,
   author = "J. Bertrand",
   year = "1855",
   title = "Sur la m\'ethode des moindres carr\'es",
   journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
   volume = "40",
   pages = "1190--1192",
   kwds = "la, Gauss, lsq, history"
}

@article{becr:88,
   author = "R. Bevilacqua and B. Codenotti and F. Romani",
   year = "1988",
   title = "Parallel Solution of Block Tridiagonal Linear Systems",
   journal = "Linear Algebra and Its Applications",
   volume = "104",
   pages = "39-58",
   kwds = "nla, prll, tridiagonal matrix"
}

-bf- -bg- -bh-

@article{bhdm:83,
   author = "R. Bhatia and C. Davis and A. McIntosh",
   year = "1983",
   title = "Perturbation of Spectral Subspaces and Solution of Linear
             Operator Equations",
   journal = "Linear Algebra and Its Applications",
   volume = "52-53",
   pages = "45--67",
   kwds = "la, pert, eig, invariant subspace, normal matrix"
}

@article{bhda:84,
   author = "R. Bhatia and C. Davis",
   year = "1984",
   title = "A Bound for the Spectral Variation of a Unitary Operator",
   journal = "Linear and Multilinear Algebra",
   volume = "15",
   pages = "71--76",
   kwds = "la, pert, eig, orthogonal matrix"
}

@article{bhho:85,
   author = "R. Bhatia and J. A. R. Holbrook",
   year = "1985",
   title = "Short Normal Paths and Spectral Variation",
   journal = "Proceedings of the American Mathematical Society",
   volume = "94",
   pages = "377--382",
   kwds = "la, pert, eig, orthogonal matrix, normal matrix"
}

@book{bhat:87,
   author = "R. Bhatia",
   year = "1987",
   title = "Perturbation Bounds for Matrix Eigenvalues",
   series = "Pitman Research Notes in Mathematics",
   publisher = "Longmann Scientific \& Technical",
   address = "Harlow, Essex",
   note = "Published in the USA by John Wiley.",
   kwds = "book, la, pert, eig"
}

@unpublished{bhdk:87,
   author = "R. Bhatia and C. Davis and P. Koosis",
   year = "1987",
   title = "An Extremal Problem in {Fourier} Analysis with Applications
             to Operator Theory",
   note = "Preprint cited in \cite{bhat:87}",
   kwds = "la, functional analysis, invariant subspace"
}

@article{bhdk:91,
   author = "R. Bhatia and C. Davis and F. Kittaneh",
   year = "1991",
   title = "Some Inequalities for Commutators and an Application
             to Spectral Variation",
   journal = "Aequationes Mathematicae",
   volume = "41",
   pages = "70--78",
   kwds = "la, eig, pert, symmetric matrix, orthogonal matrix"
}

@unpublished{bhbh:91,
   author = "R. Bhatia and T. Bhattacharyya",
   year = "1991",
   title = "A {Henrici} Theorem for Joint Spectra of Commuting Matrices",
   note = "Manuscript, Indian Statistical Institute.",
   kwds = "la, eig, pert, Clifford algebra, commuting matrices"
}

@unpublished{bhbh:91a,
   author = "R. Bhatia and T. Bhattacharyya",
   year = "1991",
   title = "A Generalization of the {Hoffman--Wielandt} Theorem",
   note = "Manuscript, Indian Statistical Institute.",
   kwds = "la, eig, pert, Clifford algebra, commuting matrices"
}

@unpublished{bhat:92,
   author = "R. Bhatia",
   year = "1992",
   title = "On Residual Bounds for Eigenvalues",
   note = "Manuscript, Indian Statistical Institute.",
   kwds = "la, eig, pert, residual bound"
}

-bi-

@article{bipa:88,
   author = "D. Bini and V. Pan",
   year = "1988",
   title = "Efficient Algorithms for the Evaluation of the Eigenvalues
             of (Block) Banded {Toeplitz} Matrices",
   journal = "Mathematics of Computation",
   volume = "50",
   pages = "431-448",
   kwds = "nla, prll, Toeplitz matrix, fast algorithm"
}

@article{birk:46,
   author = "G. D. Birkhoff",
   year =  "1946",
   title = "Tres Observaciones Sobre el Algebra Lineal",
   journal = "Universidad Nacional de Tucuman Revista, Serie A",
   volume = "5",
   pages = "147--151",
   annote = "{The citation to K\"onig is the same as in Hall.}",
   kwds = "la, convexity, doubly stochastic matrix"
}

@incollection{bivl:86,
   author = "C. H. Bischof and Van Loan, C.",
   year = "1986",
   title = "Computing the {SVD} on a Ring of Array Processors",
   booktitle = "Large Scale Eigenvalue Problems",
   editor = "J. Cullum and R. Willoughby",
   publisher = "North-Holland",
   pages = "51--66",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, svd, prll"
}

@incollection{bisc:87,
   author = "C. H. Bischof",
   year = "1987",
   title = "The Two-Sided Block {J}acobi Method on Hypercube Architectures",
   booktitle = "Hypercube Multiprocessors",
   editor = "M. T. Heath",
   publisher = "{SIAM} Publications",
   address = "Philadelphia",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, Jacobi's method, block algorithm, prll, hypercube"
}

@article{bivl:87,
   author = "C. H. Bischof and C. Van Loan",
   year = "1987",
   title = "The {$WY$} Representation for Products of
             {Householder} Transformations",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "8",
   pages = "s2-s13",
   kwds = "nla, prll, Householder transformation, qrd,
            memory hierarchy"
}

@techreport{bisc:88,
   author = "C. H. Bischof",
   year = "1988",
   title = "Computing the Singular Value Decomposition on a
             Distributed System of Vector Processors",
   number = "87 869",
   institution = "Computer Science Department, Cornell University",
   address = "Ithaca, NY",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, svd, prll"
}

@phdthesis{bisc:88a,
   author = "C. H. Bischof",
   year = "1988",
   title = "{QR} Factorization Algorithms for Coarse Grain
            Distributed Systems",
   school = "Computer Science, Cornell University",
   address = "Ithaca, NY",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, qrd, prll"
}

@inproceedings{bisc:89,
   author = "C. H. Bischof",
   year = "1989",
   title = "A Block {QR}~Factorization Algorithm Using Restructed
             Pivoting",
   booktitle = "SUPERCOMPUTING '89",
   pages = "248--256",
   publisher = "ACM Press",
   address = "New York",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, qrd, block algorithm, rank determination"
}

@techreport{biha:89,
   author = "C. H. Bischof and P. C. Hansen",
   year = "1989",
   title = "Structure-Preserving and Rank-Revealing {QR}-Factorizations",
   institution = "Mathematics and Computer Science Division,
                   Argonne National Laboratory",
   type = "Preprint",
   number = "MCS-P100-0989",
   kwds = "nla, condition estimation"
}

@techreport{bilp:89,
   author = "C. H. Bischof and J. G. Lewis and D. J. Pierce",
   year = "1989",
   title = "Incremental Condition Estimation for General Matrices",
   institution = "Mathematics and Computer Science Division,
                   Argonne National Laboratory",
   type = "Preprint",
   number = "MCS-P106-0989",
   kwds = "nla, condition estimation"
}

@article{bisc:90,
   author = "C. H. Bischof",
   year = "1990",
   title = "Incremental Condition Estimation",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "11",
   pages = "312--322",
   kwds = "nla, condition estimation"
}

@techreport{bisc:90a,
   author = "C. H. Bischof",
   year = "1990",
   title = "Adaptive Condition Estimation for Rank-one Updates of {QR} 
	Factorizations",
   institution = "Argonne National Laboratory, Mathematics
                   and Computer Sciences Division",
   type = "Technical Report",
   number = "ANL/MCS-P166-0790",
   kwds = "nla, condition estimation, qrd"
}

@article{bipl:90,
   author = "C. H. Bischof and D. J. Pierce and J. G. Lewis",
   year = "1990",
   title = "Incremental Condition Estimation for Sparse Matrices",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "11",
   pages = "644--659",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, condition estimation, sparse"
}

@techreport{bipt:90,
   author = "C. H. Bischof and C.-T. Pan and P. T. P. Tang",
   year = "1990",
   title = "Stable {Cholesky} Up- and Downdating Algorithms
             for Systolic and SIMD Architectures",
   institution = "Mathematics and Computer Science Division,
                   Argonne National Laboratory",
   type = "Preprint",
   number = "MCS-P167-00790",
   kwds = "nla, prll, updating, Cholesky decomposition,
            systolic, simd"
}

@article{bisc:91,
   author = "C. H. Bischof",
   year = "1991",
   title = "A Parallel {QR}~Factorization Algorithm with
            Controlled Local Pivoting",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "12",
   pages = "36--57",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, qrd, rank determination"
}

@article{biha:91,
   author = "C. H. Bischof and P. C. Hansen",
   year = "1991",
   title = "Structure Preserving and Rank-Revealing {QR}~Factorizations",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "12",
   pages = "1332--1350",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, qrd, sparse, rank determination"
}

@article{bish:91,
   author = "C. H. Bischof and G. M. Shroff",
   year = "1991",
   title = "On Updating Signal Subspaces",
   journal = "IEEE Transactions on Signal Processing",
   volume = "40",
   pages = "96--105",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, signal processing, rank determination"
}

@techreport{biha:91a,
   author = "C. H. Bischof and P. C. Hansen",
   year = "1991",
   title = "A Block Algorithm for Computing
            Rank-Revealing {QR}-Factorizations",
   institution = "Mathematics and Computer Science Division,
                  Argonne National Laboratory",
   type = "Reprot",
   number = "MCS-P251-0791",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, qrd, rank determination, block algorithm"
}

@book{bifh:75,
   author = "Yvonne M. M. Bishop and Stephen E. Fienberg
              and Paul W. Holland",
   year = "1975",
   title = "Discrete Multivariate Analysis",
   publisher = "MIT Press",
   address = "Cambridge, Massachusetts",
   kwds = "book, stat, log-linear model, categorical data,
           multivariate analysis"
}

@techreport{bitn:79,
   author = "James R. Bitner",
   year = "1979",
   title = "Algorithms for Storing Matrices on Disk to Minimize Access Time",
   institution = "Department of Computer Science,
                   The University of Texas at Austin",
   type = "Technical Report",
   number = "TR-99",
   kwds = "nla, memory hierarchy"
}

@article{bidh:84,
   author = "Dina Bitton and David J. DeWitt and David K. Hsiao and
              Jaishankar Menon",
   year = "1984",
   title = "A Taxonomy of Parallel Sorting",
   journal = "Computing Surveys",
   volume = "16",
   pages = "287-318",
   kwds = "prll, sorting"
}

-bj-

@article{bjer:51,
   author = "A. Bjerhammer",
   year = "1951",
   title = "Rectangular Reciprocal Matrices with Special Reference
             to Geodetic Calculations",
   journal = "Bulletin G\'eod\'esique",
   volume = "52",
   pages = "118-220",
   kwds = "la, ginv, lsq"
}

@article{bjor:67,
   author = "{\AA}. Bj{\"o}rck",
   year = "1967",
   title = "Solving Linear Least Squares Problems by {Gram--Schmidt} 
             Orthogonalization",
   journal = "BIT",
   volume = "7",
   pages = "1-21",
   kwds = "nla, lsq, qrd, Gram-Schmidt algorithm"
}

@article{bjgo:67,
   author = "{\AA}. Bj{\"o}rk and G. H. Golub",
   year = "1967",
   title = "Iterative Refinement of Linear Least Squares Solution
             by Householder Transformation",
   journal = "BIT",
   volume = "7",
   pages = "322--337",
   kwds = "nla, lsq, iterative refinement, Householder transformation"
}

@article{bjor:67a,
   author = "{\AA}. Bj{\"o}rck",
   year = "1967",
   title = "Iterative Refinement of Linear Least Squares Solutions {I}",
   journal = "BIT",
   volume = "7",
   pages = "257--278",
   kwds = "nla, lsq, iterative refinement"
}

@article{bjor:67b,
   author = "{\AA}. Bj{\"o}rck",
   year = "1967",
   title = "Contribution no.~22. {Iterative} Refinement of Linear Least
             Squares Solutions by {Householder} Transformations",
   journal = "BIT",
   volume = "7",
   pages = "322--337",
   kwds = "nla, lsq, iterative refinement, Householder transformation"
}

@article{bjor:68,
   author = "{\AA}. Bj{\"o}rck",
   year = "1968",
   title = "Iterative Refinement of Linear Least Squares Solutions {II}",
   journal = "BIT",
   volume = "8",
   pages = "8-30",
   kwds = "nla, lsq, iterative refinement"
}

@article{bjpe:70,
   author = "{\AA}. Bj{\"o}rck and V. Pereyra",
   year = "1970",
   title = "Solution of {V}andermonde Systems of Equations",
   journal = "Mathematics of Computation",
   volume = "24",
   pages = "893--903",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Vandermonde matrix, linear system"
}

@article{bjor:71,
   author = "{\AA}. Bj{\"o}rck and C. Bowie",
   year = "1971",
   title = "An Iterative Algorithms for Computing the Best Estimate of
             an Orthogonal Matrix",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "8",
   pages = "358--364",
   kwds = "nla, svd, orthogonal matrix"
}

@article{bjel:73,
   author = "{\AA}. Bj{\"o}rck and Tommy Elfving",
   year = "1973",
   title = "Algorithms for Confluent {Vandermonde} Systems",
   journal = "Numerische Mathematik",
   volume = "21",
   pages = "130--137",
   kwds = "nla, Vandermonde matrix"
}

@article{bjgo:73,
   author = "{\AA}. Bj{\"o}rck and G. H. Golub",
   year = "1973",
   title = "Numerical Methods for Computing Angles between Linear Subspaces",
   journal = "Mathematics of Computation",
   volume = "27",
   pages = "579-594",
   kwds = "math, nla, gsvd, canonical angles, subspace metric"
}

@inproceedings{bjor:76,
   author = "{\AA}. Bj{\"o}rck",
   year = "1976",
   title = "Methods for Sparse Least Squares Problems",
   pages = "177-199",
   booktitle = "Sparse Matrix Computations",
   editor = "J.R. Bunch and D. J. Rose",
   publisher = "Academic Press",
   address = "New York",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, sparse"
}

@article{bjor:78,
   author = "{\AA}. Bj{\"o}rck",
   year = "1978",
   title = "Comment on the Iterative Refinement of Least Squares Solutions",
   journal = "Journal of the American Statistical Association",
   volume = "73",
   pages = "161--166",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, iterative refinement"
}

@inproceedings{bjor:79,
   author = "{\AA}. Bj{\"o}rck",
   year = "1979",
   title = "{SSOR} Preconditioning Methods for Sparse Least Squares Problems",
   pages = "21--25",
   booktitle = "In Proceedings of the Computer Science and Statistics
	12th Annual Symposium on the Interface", 
   publisher = "University of Waterloo, Canada",
   address = "",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, relaxation, preconditioning"
}

@article{bjel:79,
   author = "{\AA}. Bj{\"o}rck and Tommy Elfving",
   year = "1979",
   title = "Accelerated Projection Methods for Computing Pseudoinverse
             Solutions of Systems of Linear Equations",
   journal = "BIT",
   volume = "19",
   pages = "145--163",
   kwds = "nla, ginv, linear system, iter"
}

@techreport{bjel:79,
   author = "{\AA}. Bj{\"o}rck and L. Eld\'en",
   year = "1979",
   title = "Methods in numerical algebra for ill-posed problems",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Technical Report",
   number = "LiTH-MAT-R-1979-33",
   kwds = "nla, linear system, regularization, ill-posed problem"
}

@article{bjgu:80,
   author = "{\AA}. {Bj\"orck} and I. S. Duff",
   year = "1980",
   title = "A Direct Method for the Solution of Sparse Linear Least Squares 
             Problems",
   journal = "Linear Algebra and Its Applications",
   volume = "34",
   pages = "43-68",
   kwds = "nla, lsq, sparse"
}

@book{bjpl:81,
   author = "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider",
   year = "1981",
   title = "Large--Scale Matrix Problems",
   publisher = "North-Holland",
   address = "New York",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "book, nla, sparse"
}

@article{bjha:83,
   author = "{\AA}. Bj{\"o}rck and S. Hammarling",
   year = "1983",
   title = "A {S}chur Method for the Square Root of a Matrix",
   journal = "Linear Algebra and Its Applications",
   volume = "52/53",
   pages = "127--140",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, matrix function, matrix square root"
}

@article{bjor:84,
   author = "{\AA}. Bj{\"o}rck",
   year = "1984",
   title = "A General Updating Algorithm for Constrained Linear Least Squares 
	problems", 
   journal = " SIAM Journal on Scientific and  Statistical Computing",
   volume = "5",
   pages = "394--402.",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, sparse, updating, constraints"
}

@article{bjor:87,
   author = "{\AA}. Bj{\"o}rck",
   year = "1987",
   title = "Stability Analysis of the Method of Seminormal Equations",
   journal = "Linear Algebra and its Applications",
   volume = "88/89",
   pages = "31--48",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lsq, rounding error, normal equations"
}

@techreport{bjor:87a,
   author = "{\AA}. Bj{\"o}rck",
   year = "1987",
   title = "Least Squares Methods",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Working paper",
   number = "",
   note = "To appear in {\it Handbook of Numerical Analysis, V.1:
           Solution of Equations in $R^n$}, P. G. Ciarlet and J. L.
           Lions editors, Elsevier, North Holland",
   kwds = "math, na, nla, lsq, regr"
}

@book{bjor:88,
   author = "{\AA}. Bj{\"o}rck",
   year = "1988",
   title = "Solution of Equations in {$R^N$}",
   series = "Least Squares Methods: Handbook of Numerical Analysis",
   volume = "1",
   publisher = "North-Holland",
   note = "Cited in \cite{govl:89}.",
   kwds = "book, nla, lsq"
}

@techreport{bjor:88a,
   author = "{\AA}. Bj{\"o}rck",
   year = "1988",
   title = "Error Analysis of Least Squares Algorithms",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Technical Report",
   number = "LiTH-MAT-R-1988-22",
   kwds = "nla, lsq, rounding error, pert"
}

@article{bjor:88b,
   author = "{\AA}. Bj{\"o}rck",
   year = "1988",
   title = "A Bidiagonalization Algorithm for Solving Ill-Posed System
            of Linear Equations",
   journal = "BIT",
   volume = "28",
   pages = "659--670",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, linear system, sparse, Lanczos algorithm, bidiagonalization,
           ill-posed system, regularization"
}

@article{bjor:88b,
   author = "{\AA}. Bj{\"o}rck",
   year = "1988",
   title = "A Direct Method for Sparse Least Squares Problems with lower and 
	Upper Bounds",
   journal = " Numerische Mathematik",
   volume = "54",
   pages = "19--32",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, constraints"
}

@techreport{bjor:89,
   author = "{\AA}. Bj{\"o}rck",
   year = "1989",
   title = "Componentwise Backward Errors and Condition Estimates for
             Linear Least Square Problems",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Technical Report",
   number = "LiTH-MATH-R-1989-13",
   kwds = "la, nla, lsq, pert, backward perturbation"
}

@techreport{bjor:90,
   author = "{\AA}. Bj{\"o}rck",
   year = "1990",
   title = "Error Analysis of the Modified {Gram--Schmidt} Method
             for Solving Underdetermined Linear Systems",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Technical Report",
   number = "LiTH-MAT-R-1990-06",
   kwds = "nla, Gram-Schmidt algorithm, rounding error"
}

@inproceedings{bjor:90a,
   author = "{\AA}. Bj{\"o}rck",
   year = "1990",
   title = "Iterative Refinement and Reliable Computing",
   pages = "249--266",
   booktitle = "Reliable Numerical Computation",
   editor = "M. G. Cox and S. J. Hammarling",
   publisher = "Clarendon Press",
   address = "Oxford",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, iterative refinement"
}

@unpublished{bjor:90b,
   author = "{\AA}.  Bj{\"o}rck",
   year = "1990",
   title = "The Householder Symposium:  Meeting on Numerical Algebra",
   note ="Abstracts of the Symposium.  Compiled by {\AA}ke Bj{\"o}rk,
    Department of Mathematics, Link{\"o}ping University",
   kwds = "nla, Householder Symposium"
}

@incollection{bjor:90c,
   author = "{\AA}. Bj{\"o}rck",
   year = "1990",
   title = "Least Squares Methods",
   editor = "P. G. Ciarlet and J. L. Lions",
   booktitle = "Handbook of Numerical Analysis", 
   publisher = "Elsevier/North Holland",
   volume = "I: Finite Difference Methods-Solution of Equations in $R^n$",
   address = "Amsterdam",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq"
}

@inproceedings{bjor:91,
   author = "{\AA}. Bj{\"o}rck",
   year = "1991",
   title = "Error Analysis of Least Squares Algorithms",
   pages = "41--73",
   booktitle = "Numerical Linear Algebra, Digital Signal Processing
	and Parallel Algorithms", 
   series = "NATO ASI Series",
   editor = "G. H. Golub and P. Van Dooren",
   publisher = "Springer",
   address = "Berlin",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, rounding error, signal processing"
}

@article{bjpa:92,
   author = "{\AA}. Bj{\"o}rck and C. C. Paige",
   year = "1992",
   title = "Loss and Recapture of Orthogonality in the Modified {Gram-Schmidt}
	Algorithm",
   journal = "SIAM J. Matrix Anal. Appl.",
   volume = "13",
   pages = "176--190",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, orthogonalization, Gram-Schmidt algorithm, rounding error"
}

@article{bjor:91a,
   author = "{\AA}. Bj{\"o}rck",
   year = "1991",
   title = "Component-wise Perturbation Analysis and Errors Bounds for
            Linear Least Square Solutions",
   journal = "BIT",
   volume  = "31",
   pages = "238--244",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, lsq, structured perturbation, pert"
}

@techreport{bjor:91b,
   author = "{\AA}. Bj{\"o}rck",
   year = "1991",
   title = "Pivoting and Stability in the Augmented System Method",
   institution = "Department of Mathematics, Link{\"o}ping University",
   type = "Report",
   number = "LiTH-MAT-R-1991-30",
   kwds = "nla, rounding error, lsq"
}

-bk- -bl-

@article{blst:74,
   author = "M. M. Blevins and G. W. Stewart",
   year = "1974",
   title = "Calculating Eigenvectors of Diagonally Dominant
             Matrices",
   journal = "Journal of the ACM",
   volume = "21",
   pages = "261--271",
   kwds = "nla, eig, diagonal dominance"
}

@article{blue:78,
   author = "J. L. Blue",
   year = "1978",
   title = "A Portable Fortran Program to Find the Euclidean Norm of a Vector",
   journal = "Transactions on Mathematical Software",
   volume = "4",
   pages = "15-23",
   kwds = "nla, blas, software, norm"
}

@article{blum:67,
   author = "E. K. Blum",
   year = "1967",
   title = "The Computation of Eigenvalues and Eigenvectors of a
            Completely Continuous Self-Adjoint Operator",
   journal = "J. Comput. Syst. Sci.",
   volume = "1",
   pages = "362--370",
   kwds = "nla, eig, sparse"
}

-bm- -bn- -bo-

@techreport{bobu:63,
   author = "D. Bogert and W. R. Burris",
   year = "1963",
   title = "Comparison of Least Squares Algorithms",
   institution = "Neutron Physics Division,
                   Oak Ridge National Laboratory",
   type = "Report",
   number = "ORNL-3499",
   note = "Vol. 1, Sec. 5.5",
   kwds = "nla, lsq, qrd"
}

@article{bobs:87,
   author = "P. T. Boggs and R. H. Byrd and R. B. Schnabel",
   year = "1987",
   title = "A Stable and Efficient Algorithm for Nonlinear
            Orthogonal Regression",
   journal = " SIAM Journal on Scientific and  Statistical Computing",
   volume = "8",
   pages = "1052--1078",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nlop, lsq, nllsq"
}


@article{boht:75,
   author = "Z. Bohte",
   year = "1975",
   title = "Bounds for Rounding Errors in the {G}aussian Elimination for Band
            Systems",
   journal = "Journal of the Institute of Mathematics and its Applications",
   volume = "16",
   pages = "133--142",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, band matrix, rounding error"
}

@article{bobr:86,
   author = "A. Bojanczyk and R. P. Brent",
   year = "1986",
   title = "Parallel Solution of Certain {Toeplitz} Least-Squares
             Problems",
   journal = "Linear Algebra and Its Applications",
   volume = "77",
   pages = "43-60",
   kwds = "nla, systolic, prll, Toeplitz matrix, lsq"
}

@article{bobh:86,
   author = "A. Bojanczyk and R. P. Brent and F. de Hoog",
   year = "1986",
   title = "{QR} Factorization of Toeplitz Matrices",
   journal = "Numerische Mathematik",
   volume = "49",
   pages = "81--94",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, qrd, Toeplitz matrix"
}

@article{bobv:87,
   author = "A. Bojanczyk and R. P. Brent and P. Van Dooren and F. de Hoog",
   year = "1987",
   title = "A Note on Downdating the {Cholesky} Factorization",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "8",
   pages = "210--221",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, Cholesky decomposition, updating"
}

@article{bogu:84,
   author = "D. L. Boley and G. H. Golub",
   year = "1984",
   title = "The {Lanczos--Arnoldi} Algorithm and Controllability",
   journal = "Systems and Control Letters",
   volume = "4",
   pages = "317--324",
   kwds = "nla, controllability, Lanczos algorithm, Arnoldi's method"
}

@article{bolu:86,
   author = "D. L. Boley and W.-S. Lu",
   year = "1986",
   title = "Measuring How Far a Controllable System is from an
             Uncontrollable One",
   journal = "IEEE Transactions on Automatic Control",
   volume = "AC-31",
   pages = "249--251",
   kwds = "nla, condition, controllability"
}

@inproceedings{bogs:91,
   author = "E. C. Boman and M. F. Griffen and G. W. Stewart",
   year = "1991",
   title = "Direction of Arrival and The Rank-Revealing URV Decomposition",
   booktitle = "Procedings of ACASSP-91",
   publisher = "IEEE",
   address = "Washington, DC",
   kwds = "nla, signal processing, direction of arrival, urvd"
}

@article{bobo:88,
   author = "A. D. Booth and I. J. M. Booth",
   year = "1988",
   title = "A Note on the Progressive Calculation of the Mean
             and Variance",
   journal = "Journal of Computational Physics",
   volume = "77",
   pages = "537--539",
   kwds = "stat, mean, variance, update, software"
}

@article{boot:70,
   author = "J. Boothroyd",
   year = "1970",
   title = "The {QR}~Algorithm for Symmetric Tridiagonal Matrices
             Using a Semi-implicit Shift of the Orgin",
   journal = "Australian Computer Journal",
   volume = "2",
   pages = "55--60",
   kwds = "nla, eig, QR algorithm, tridiagonal matrix, symmetric matrix"
}

@article{borc:1857,
   author = "C. W. Borchart",
   year = "1857",
   title = " {Bemerkung \"uber die beiden vorstehenden Aufs\"atze}",
   journal = " {Journal f\"ur die reine und angewandte Mathematik}",
   volume = "53",
   pages = "281-283",
   kwds = "la, inertia, Sylvester-Jacobi inertia theorem"
}

@article{bors:70,
   author = "W. B{\"o}rsch-Supan",
   year = "1970",
   title = " {Residuenabsch\"atzung f\"ur Polynom-Nullstellen
               Mittels Lagrange-Interpolation}",
   journal = "Numerische Mathematik",
   volume = "287--296",
   pages = "287--296",
   kwds = "nlop, polynomial, pert, interpolation"
}

@book{bood:71,
   author = "T. L. Boullion and P. L. Odell",
   year = "1971",
   title = "Generalized Inverse Matrices",
   publisher = "John Wiley \& Sons",
   address = "New York",
   kwds = "book, la, ginv"
}

@article{bmpw:66,
   author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H. Wilkinson",
   year = "1966",
   title = "Solution of Real and Complex Systems of Linear Equations",
   journal = "Numerische Mathematik",
   volume = "8",
   pages = "217--234",
   note = "Also in \cite[pp.92--110]{wire:71}.",
   kwds = "nla, lud, linear system, software"
}

@article{bmrw:68,
   author = "H. J. Bowdler and R. S. Martin and C. Reinsch and
              J. H. Wilkinson",
   year = "1968",
   title = "The {QR}~and {LR}~Algorithms for Symmetric Matrices",
   journal = "Numerische Mathematik",
   volume = "11",
   pages = "293--306",
   note = "Also in \cite[pp.227--240]{wire:71}.",
   kwds = "nla, eig, QR algorithm, symmetric matrix, software"
}

@article{bohu:59,
   author = "G. E. P. Box and J. S. Hunter",
   year = "1959",
   title = "Condensed Calculations for Evolutionary Operation Programs",
   journal = "Technometrics",
   volume = "1",
   pages = "77-95",
   kwds = "stat, na"
}

@book{boye:68,
   author = "C. B. Boyer",
   year = "1968",
   title = "A History of Mathematics",
   publisher = "John Wiley \& Sons",
   address = "New York",
   kwds = "book, math, history"
}

@book{bbdg:87,
   author = "J. Boyle and R. Butler and T. Disz and B. Glickfield and E. Lusk
            and R. Overbeek and J. Patterson and R. Stevens",
   year = "1987",
   title = "Portable Programs for Parallel Processors",
   publisher = "Holt, Rinehart and Winston",
   note = "Cited in \cite{govl:89}.",
   kwds = "book, cs, prll"
}

-bp- -bq- -br-

@article{brfl:66,
   author = "W. W. Bradbury and R. Fletcher",
   year = "1966",
   title = "New Iterative Methods for Solution of the Eigenproblem",
   journal = "Numerische Mathematik",
   volume = "9",
   pages = "259--267",
   kwds = "nla, eig, sparse, conjugate gradients"
}

@article{brsr:79,
   author = "R. A. Bradley and S. S. Srivastva",
   year = "1979",
   title = "Correlation in Polynomial Regression",
   journal = "American Statistician",
   volume = "33",
   pages = "11-14",
   kwds = "stat, regr, correlation, polynomial"
}

@article{brps:86,
   author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
   year = "1986",
   title = "The construction of Preconditioners for Elliptic Problems by
            Substructuring {I}",
   journal = "Mathematics of Computation",
   volume = "47",
   pages = "103--134",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, preconditioning"
}

@article{brps:86a,
   author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
   year = "1986",
   title = "The construction of Preconditioners for Elliptic Problems by
            Substructuring {II}",
   journal = "Mathematics of Computation",
   volume = "49",
   pages = "1--17",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, preconditioning"
}

@phdthesis{bram:89,
   author = "R. B. Bramley",
   year = "1989",
   title = "Row Projection Methods for Linear Systems",
   school = "Center for Supercomputing Research and Development,
              University of Illinois",
   kwds = "nla, sparse, linear system, Kaczmarz's method, projection method,
            Cimmino's method"
}

@techreport{brsa:90,
   author = "R. Bramley and A. Sameh",
   year = "1990",
   title = "Row Projection Methods for Large Nonsymmetric Linear Systems",
   institution = "Center for Supercomputing Research and Development",
   adress  = "University of Urbana, Illinois",
   type = "Report",
   number = "No. 957",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, linear system, sparse, prll, projection method"
}

@article{brpa:86,
   author = "A. Brass and G. S. Pawley",
   year = "1986",
   title = "Two and Three Dimensional {FFT}s on Highly
            Parallel Compters",
   journal = "Parallel Computing",
   volume = "3",
   pages = "167-184",
   kwds = "prll, systolic, fft, fast algorithm"
}

@article{brro:69,
   author = "Alfred Brauer and Hans Rohrbach",
   year = "1969",
   title = " {Einige Anwendungen der Matrizentheorie auf
               algebraische Gleichungen}",
   journal = " {Journal f\"ur die reine und angewandte Mathematik}",
   volume = "236",
   pages = "11--25",
   kwds = "la, nlop, eig, pert, polynomial"
}

@techreport{bren:70,
   author = "R. P. Brent",
   year = "1970",
   title = "Algorithms for Matrix Multiplication",
   institution = "Computer Science Department, Stanford University",
   type = "Technical Report",
   number = "STAN-CS-70-157",
   kwds = "nla, matrix multiplication, fast algorithm, rounding error"
}

@article{bren:70a,
   author = "R. P. Brent",
   year = "1970",
   title = "Error Analysis of Algorithms for Matrix Multiplication
             and Triangular Decomposition using Winograd's Identity",
   journal = "Numerische Mathematik",
   volume = "16",
   pages = "145--156",
   note = "Cited in \cite{high:89b}",
   kwds = "nla, matrix multiplication, fast algorithm, rounding error"
}

@article{bren:72,
   author = "R. P. Brent",
   year = "1972",
   title = "On the {Davidenko--Branin} Method for Solving Simultaneous
             Nonlinear Equations",
   journal = "IBM Journal of Research and Development",
   volume = "16",
   pages = "434--436",
   kwds = "nlop"
}

@article{bren:73,
   author = "R. P. Brent",
   year = "1973",
   title = "Some Efficient Algorithms for Solving Systems of
             Nonlinear Equations",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "10",
   pages = "327--344",
   kwds = "nlop"
}

@article{brlu:8?,
   author = "R. P. Brent and F. T. Luk",
   year = "19??",
   title = "A Systolic Array for the Linear-Time Solution of {Toeplitz}
             Systems of Equations",
   journal = "Journal of VLSI and Computer Systems",
   volume = "1",
   pages = "1--22",
   kwds = "nla, prll, Toeplitz matrix, systolic"
}

@article{brlu:85,
   author = "R. P. Brent and F. T. Luk",
   year = "1985",
   title = "The Solution of Singular-Value and Symmetric Eigenvalue
             Problems on Multiprocessor Arrays",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "6",
   pages = "69--84",
   kwds = "nla, prll, svd, eig, symmetric matrix, systolic"
}

@article{brlv:8?,
   author = "R. P. Brent and F. T. Luk and Van Loan, C.",
   year = "198?",
   title = "Computation of the Singular Value Decomposition
             Using Mesh-Connected Processors",
   journal = "Journal of VLSI and Computer Systems",
   volume = "1",
   pages = "242--270",
   kwds = "nla, prll, svd, systolic"
}

@book{brez:80,
   author = "C. Brezinski",
   year = "1980",
   title = "Pad\'e-Type Approximations and General Orthogonal
             Polynomials",
   publisher = "Birkh{\"a}user",
   address = "Basel",
   kwds = "book, na, nla, Pade table, orthogonal polynomial"
}

@article{broc:81,
   author = "H. K. Brock and B. J. Brooks and F. Sullivan",
   year = "1981",
   title = "Diamond a Sorting Method for Vector Machines",
   journal = "BIT",
   volume = "21",
   pages = "142--152",
   kwds = "prll, sorting"
}

@article{brpo:75,
   author = "K. W. Brodlie and M. J. D. Powell",
   year = "1975",
   title = "On the Convergence of Cyclic {J}acobi Methods",
   journal = "Journal of the Institute of Mathematics and its Applications",
   volume = "15",
   pages = "279--287",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, Jacobi's method"
}

@article{brjo:74,
   author = "O. E. Br{\o}nlund and L. Johnsen",
   year = "1974",
   title = "{QR}-Factorization of Partitioned Matrices",
   journal = "Computer Methods in Applied Mechanics and Engineering",
   volume = "3",
   pages = "143-172",
   kwds = "nla, qrd"
}

@article{broo:87,
   author = "E. D. Brooks III",
   year = "1987",
   title = "A Butterfly Processor-Memory Interconnection
             for a Vector Processing Environment",
   journal = "Parallel Computing",
   volume = "4",
   pages = "103-110",
   kwds = "prll, shared memory, vect"
}

@article{brde:68,
   author = "K. M. Brown and J. E. Dennis",
   year = "1968",
   title = "On {Newton}-Like Iteration Functions: General Convergence
             Theorems and a Specific Algorithm",
   journal = "Numerische Mathematik",
   volume = "12",
   pages = "186--191",
   kwds = "nlop, Newton's method"
}

@article{brkr:74,
   author = "G. F. Brown and J. B. Kadane and J. G. Ramage",
   year = "1974",
   title = "The Asymptotic Bias and Mean-Squared Error of Double
             {$K$}-class Estimators when the Distrubances are Small",
   journal = "International Economic Review",
   volume = "15",
   pages = "667--679",
   kwds = "stat, regr, pert, eriv"
}

@article{brow:28,
   author = "E. T. Browne",
   year = "1928",
   title = "The Characteristic Equations of a Matrix",
   journal = "Bulletin of the American Mathematical Society",
   volume = "34",
   pages = "363-368",
   kwds = "la, eig"
}

@article{brow:30,
   author = "E. T. Browne",
   year = "1930",
   title = "The Characteristic Roots of a Matrix",
   journal = "Bulletin of the American Mathematical Society",
   volume = "36",
   pages = "708-710",
   kwds = "la, eig"
}

@inproceedings{brow:85,
   author = "J. C. Browne",
   year = "1985",
   title = "Formulation and Programming of Parallel Computations:
             A Unified Approach",
   booktitle = "Proceedings of the 1978 International Conference
                 on Parallel Processing",
   editor = "D. Degroot",
   pages = "624-631",
   publisher = "IEEE Computer Society Press",
   address = "Wahsington, DC",
   kwds = "prll"
}

@book{brow:65,
   author = "K. A. Brownlee",
   year = "1965",
   title = "Statistical Theory and Methodology in Science and Engineering",
   publisher = "John Wiley",
   address = "New York",
   kwds = "book, stat"
}

@article{broy:65,
   author = "C. G. Broyden",
   year = "1965",
   title = "A Class of Methods for Solving Nonlinear Simultaneous Equations",
   journal = "Mathematics of Computation",
   volume = "19",
   pages = "577--593",
   kwds = "nlop, quasi-Newton"
}

@article{broy:67,
   author = "C. G. Broyden",
   year = "1967",
   title = "Quasi-{Newton} Methods and their Application to Function
             Minimization",
   journal = "Mathematics of Computation",
   volume = "21",
   pages = "368--381",
   kwds = "nlop, quasi-Newton"
}

@article{broy:69,
   author = "C. G. Broyden",
   year = "1969",
   title = "A New Method of Solving Nonlinear Simultaneous Equations",
   journal = "Computer Journal",
   volume = "12",
   pages = "1969",
   kwds = "nlop, quasi-Newton, continuation"
}

@article{broy:70,
   author = "C. G. Broyden",
   year = "1970",
   title = "The Convergence of Single-Rank Quasi-{Newton} Methods",
   journal = "Mathematics of Computation",
   volume = "24",
   pages = "365--382",
   kwds = "nlop, quasi-Newton"
}

@article{broy:73,
   author = "C. G. Broyden",
   year = "1973",
   title = "Some Condition Number Bounds for the {G}aussian Elimination
            Process",
   journal = "Journal of the Institute of Mathematics and Its Applications",
   volume = "12",
   pages = "273--286",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, condition"
}

@unpublished{brsc:82,
   year = "1982",
   author = "R. A. Brualdi and H. Schneider",
   title = "Determinantal Identities: {Gauss, Schur, Cauchy, Sylvester,
             Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley}",
   note = "Manuscript.  Department of Mathematics, University of Wisconsin",
   kwds = "la, determinant, Schur complement"
}

@book{brba:80,
   author = "S. C. Bruell and G. Balbo",
   year = "1980",
   title = "Computational Algorithms for Closed Queueing Networks",
   publisher = "North Holland",
   address = "New York",
   kwds = "book, la, queue, Markov chain"
}

-bs- -bt- -bu-

@article{buck:74,
   author = "A. Buckley",
   year = "1974",
   title = "A Note on Matrices {$A = 1 + H$}, {$H$} Skew-Symmetric",
   journal = "Zeitschrift fur Angewandte Mathematik und Mechanik",
   volume = "54",
   pages = "125--126",
   note = "Cited in \cite{govl:89}.",
   kwds = "la, skew-symmetric matrix"
}

@article{buck:77,
   author = "A. Buckley",
   year = "1977",
   title = "On the Solution of Certain Skew-Symmetric Linear Systems",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "14",
   pages = "566--570",
   note = "Cited in \cite{govl:89}.",
   kwds = "la, linear system, skew-symmetric matrix"
}

@article{bupa:71,
   author = "J. R. Bunch and B. N. Parlett",
   year = "1971",
   title = "Direct Methods for Solving Symmetric Indefinite Systems
            of Linear Equations",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "8",
   pages = "639--655",
   kwds = "nla, lud, indefinite system, linear system, symmetric matrix"
}

@article{bunc:71,
   author = "J. R. Bunch",
   year = "1971",
   title = "Analysis of the Diagonal Pivoting Method",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "8",
   pages = "656--680",
   kwds = "nla, lud, indefinite system, linear system, pivoting,
            symmetric matrix"
}

@article{bunc:71a,
   author = "J. R. Bunch",
   year = "1971",
   title = "Equilibration of Symmetric Matrices in the Max-Norm",
   journal = "Journal of the ACM",
   volume = "18",
   pages = "566--572",
   kwds = "nla, scaling, symmetric matrix"
}

@article{bunc:74,
   author = "J. R. Bunch",
   year = "1974",
   title = "Partial Pivoting Strategies for Symmetric Matrices",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "11",
   pages = "521--528",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, pivoting, symmetric matrix"
}

@proceedings{buro:76,
   editor = "J. R. Bunch and D. J. Rose",
   year = "1976",
   title = "Sparse Matrix Computations",
   publisher = "Academic Press",
   address = "New York",
   kwds = "math, nla, sparse"
}

@article{bukp:76,
   author = "J. R. Bunch and L. Kaufman and B. Parlett",
   year = "1976",
   title = "Decomposition of a Symmetric Matrix",
   journal = "Numerische Mathematik",
   volume = "27",
   pages = "95--109",
   kwds = "nla, lud, indefinite system, linear system, symmetric matrix"
}

@article{buka:77,
   author = "J. R. Bunch and L. Kaufman",
   year = "1977",
   title = "Some Stable Methods for Calculating Inertia and Solving Symmetric 
             Linear Systems",
   journal = "Mathematics of Computation",
   volume = "31",
   pages = "163-179",
   kwds = "math, nla, linear system, inertia, symmetric matrix"
}

@article{buns:78,
   author = "J. R. Bunch and C. P. Nielsen and D. C. Sorensen",
   year = "1978",
   title = "Rank One Modification of the Symmetric Eigenproblem",
   journal = "Numerische Mathematik",
   volume = "31",
   pages = "31--48",
   kwds = "nla, eig, updating, symmetric matrix"
}

@article{buni:78,
   author = "J. R. Bunch and C. P. Nielsen",
   year = "1978",
   title = "Updating the Singular Value Decomposition",
   journal = "Numerische Mathematik",
   volume = "31",
   pages = "111--129",
   kwds = "nla, svd, updating"
}

@article{bunc:82,
   author = "J. R. Bunch",
   year = "1982",
   title = "A Note on the Stable Decomposition of Skew Symmetric Matrices",
   journal = "Mathematics of Computation",
   volume = "158",
   pages = "475--480",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, skew-symmetric matrix"
}

@article{bunc:85,
   author = "J. R. Bunch",
   year = "1985",
   title = "Stability of Methods for Solving {T}oeplitz Systems of Equations",
   journal = "{SIAM} Journal on Scientific and Statistical Computing",
   volume = "6",
   pages = "349--364",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, rounding error, Toeplitz matrix, linear system"
}

@article{bunc:87,
   author = "J. R. Bunch",
   year = "1987",
   title = "The Weak and Strong Stability of Algorithms in Numerical Linear
            Algebra",
   journal = "Linear Algebra and its Applications",
   volume = "88/89",
   pages = "49--66",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, pert, rounding error"
}

@article{budv:89,
   author = "J. R. Bunch and J. Demmel and Van Loan, C. F.",
   year = "1989",
   title = "The Strong Stability of Algorithms for Solving Symmetric
             Linear Systems",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "10",
   pages = "494--499",
   kwds = "nla, pert, backward perturbation, symmetric matrix"
}

@techreport{bune:69,
   author = "O. Buneman",
   year = "1969",
   title = "A Compact Non-Iterative {P}oisson Solver",
   institution = "Institute for Plasma Research",
   address = "Stanford University, Stanford, CA",
   Number = 294,
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, direct Poisson solver"
}

@article{buns:4b,
   author = "A. Bunse-Gerstner",
   year = "1984",
   title = "An Algorithm for the Symmetric Generalized Eigenvalue Problem",
   journal = "Linear Algebra and its Applications",
   volume = "58",
   pages = "43--68",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, geig, symmetric matrix"
}

@article{bgbm:92,
   author = "A. Bunse-Gerstner and R. Byers and V. Mehrmann",
   year = "1992",
   title = "A Chart of Numerical Methods for Structured Eigenvalue
            Problems",
   journal = "SIAM Journal on Matrix Analysis and Applications",
   volume = "13",
   pages = "419--453",
   kwds = "nla, eig, J-symmetric matrix, J-orthogonal matrix"
}

@phdthesis{bure:70,
   author = "H. J. Burema",
   year = "1970",
   title = "A Geometric Proof of Convergence of the {QR}~Method",
   school = "University of Groningen",
   kwds = "nla, eig, QR algorithm"
}

@article{bude:75,
   author = "J. C. P. Bus and T. J. Dekker",
   year = "1975",
   title = "Two Efficient Algorithms with Guaranteed Convergence
             for Finding a Zero of a Function",
   journal = "ACM Transactions on Mathematical Software",
   volume = "1",
   pages = "330--345",
   kwds = "nlop"
}

@article{busi:65,
   author = "P. Businger",
   year = "1965",
   title = "Algorithm 253: Eigenvalues of a  Real Symmetric Matrix
             by the {QR}~Method",
   journal = "Communication of the ACM",
   volume = "8",
   pages = "217--219",
   kwds = "nla, eig, QR algorithm, symmetric matrix"
}

@article{bugo:65,
   author = "P. Businger and G. H. Golub",
   year = "1965",
   title = "Linear Least Squares Solutions by {Householder} Transformations",
   journal = "Numerische Mathematik",
   volume = "7",
   pages = "269--276",
   note = "Also in \cite[pp.111-118]{wire:71}",
   kwds = "nla, lsq, qrd, Householder transformation, software"
}

@article{busi:68,
   author = "P. Businger",
   year = "1968",
   title = "Matrices Which Can be Optimally Scaled",
   journal = "Numerische Mathematik",
   volume = "12",
   pages = "346--248",
   kwds = "nla, condition, scaling"
}

@article{bugo:69,
   author = "P. Businger and G. H. Golub",
   year = "1969",
   title = "Algorithm 358, Singular Value Decomposition of a Complex
             Matrix",
   journal = "Communications of the ACM",
   volume = "12",
   pages = "564--565",
   kwds = "nla, svd, software"
}

@article{busi:69,
   author = "P. A. Businger",
   year = "1969",
   title = "Reducing a Matrix to {H}essenberg Form",
   journal = "Mathematics of Computation",
   volume = "23",
   pages = "819--821",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, Hessenberg matrix"
}

@article{busi:71,
   author = "P. A. Businger",
   year = "1971",
   title = "Monitoring the Numerical Stability of {G}aussian Elimination",
   journal = "Numerische Mathematik",
   volume = "16",
   pages = "360--361",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, rounding error"
}

@article{busi:71a,
   author = "P. A. Businger",
   year = "1971",
   title = "Numerically Stable Deflation of {H}essenberg and Symmetric
            Tridiagonal Matrices",
   journal = "{BIT}",
   volume = "11",
   pages = "262--270",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, Hessenberg matrix, tridiagonal matrix, deflation"
}

@article{bugn:70,
   author = "B. L. Buzbee and G. H. Golub and C. W. Nielson",
   year = "1970",
   title = "On Direct Methods for Solving {Poisson's} Equation",
   journal = "SIAM Journal on Numerical Analysis",
   volume = "7",
   pages = "627--656",
   kwds = "nla, pde, direct Poisson solver, sparse"
}

@article{bdgg:71,
   author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub",
   year = "1971",
   title = "The Direct Solution of the Discrete {P}oisson Equation on Irregular
            Regions",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "8",
   pages = "722--736",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, pde, direct Poisson solver, sparse"
}

@article{budo:74,
   author = "B. L. Buzbee and F. W. Dorr",
   year = "1974",
   title = "The Direct Solution of the Biharmonic Equation on Rectangular
            Regions and the {P}oisson Equation on Irregular Regions",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "11",
   pages = "753--763",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, pde, fast Poisson solver, sparse"
}

@article{buzb:86,
   author = "B. L. Buzbee",
   year = "1986",
   title = "A Strategy for Vectorization",
   journal = "Parallel ",
   volume = "3",
   pages = "187--192",
   note = "Cited in \cite{govl:89}.",
   kwds = "cs, vect"
}

-bv- -bw- -bx- -by-

@phdthesis{byer:83,
   author = "R. Byers",
   year = "1983",
   title = "{H}amiltonian and Symplectic Algorithms for the Algebraic {R}iccati
            Equation",
   school = "Center for Applied Mathematics, Cornell University",
   address = "Ithaca, NY",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, eig, J-symmetric matrix, J-orthogonal matrix, Riccati equation"
}

@article{byer:84,
   author = "R. Byers",
   year = "1984",
   title = "A {L}inpack-Style Condition Estimator for the Equation
            {$AX - XB^{T} = C$}",
   journal = "{IEEE} Transactions on Automatic Control",
   volume = "AC-29",
   pages = "926--928",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, condition estimation, Sylvester equation, matrix equation"
}

@article{byna:87,
   author = "R. Byers and S. G. Nash",
   year = "1987",
   title = "On the Singular Vectors of the {L}yapunov Operator",
   journal = "{SIAM} Journal on Algebraic and Discrete Methods",
   volume = "8",
   pages = "59--66",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, svd, Lyapunov equation, matrix equation"
}

@article{bysc:86,
   author = "R. H. Byrd and R. B. Schnabel",
   year = "1986",
   title = "Continuity of the Null Space Basis and Constrained Optimization",
   journal = "Mathematical Programming",
   volume = "35",
   pages = "32--41",
   kwds = "nla, nlop, null space, constraints"
}

-bz-
-ca-

@inproceedings{cali:86,
   author = "D. A. Calihan",
   year = "1986",
   title = "Block-Oriented, Local-Memory-Based Linear Equation Solution on the
            {C}ray-2: Uniprocessor Algorithms",
   booktitle = "Proceedings of the 1986 Conference on Parallel Processing",
   pages = "375--378",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, block algorithm, linear system, vect"
}

@article{came:75,
   author = "S. L. Campbell and C. D. Meyer",
   year = "1975",
   title = "Continuity Properties of the Drazin Pseudoinverse",
   journal = "Linear Algebra and Its Applications",
   volume = "10",
   pages = "77--83",
   kwds = "la, pert, eig, ginv, Drazin generalized inverse"
}

@article{cast:85,
   author = "W. L. Cao and W. J. Stewart",
   year = "1985",
   title = "Iterative Aggregation/Disaggregation Techniques for
             Nearly Uncoupled {Markov} Chains",
   journal = "Journal of the ACM",
   volume = "32",
   pages = "702-719",
   kwds = "la, nla, Markov chain, aggregation, iter"
}

@incollection{cauc:1821,
   author = "A. L. Cauchy",
   year = "1821",
   title = "Cours d'analyse de l'\'Ecole Royale Polytechnique",
   booktitle = "Oeuvres Compl\'etes (II\,$^e$ S\'erie)",
   volume = "3",
   kwds = "la, Cauchy inequality, history"
}

@incollection{cauc:1829,
   author = "A. L. Cauchy",
   year = "1829",
   title = "Sur l'\'equation \'a l'aide de laquelle on d\'etermine les
             in\'egalit\'es s\'eculaires des mouvements des plan\`etes",
   booktitle = "Oeuvres Compl\'etes (II\,$^e$ S\'erie)",
   volume = "9",
   kwds = "la, history, eig, Cauchy interlacing theorem, symmetric matrix"
}

@article{cauc:1837,
   author = "A. Cauchy",
   year = "1837",
   title = "M\'emoire sur l'Interpolation",
   journal = "Journal de Math\'ematiques Pures et Appliqu\'ees",
   volume = "2",
   pages = "193--205",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "la, interpolation, history"
}

-cb- -cc- -cd- -ce-

@article{ceel:82,
   author = "Y. Censor and T. Elfving",
   year = "1982",
   title = "New Methods for Linear Inequalities",
   journal = "BIT",
   volume = "42",
   pages = "199--211",
   kwds = "nla, linear inequalities"
}

-cf- -cg- -ch-

@article{cham:71,
   author = "J. M. Chambers",
   year = "1971",
   title = "Regression Updating",
   journal = "Journal of the  American Statistical Association",
   volume = "66",
   pages = "744--748",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, stat, lsq, regr, updating"
}

@unpublished{cham:72,
   author = "J. M. Chambers",
   year = "1972",
   title = "Stabilizing Linear Regression against Observational Error
             in Independent Variats",
   note = "Manuscript, Bell Laboratories, Murray Hill, New Jersey.",
   kwds = "stat, svd, regr"
}

@book{cham:77,
   author = "J. M. Chambers",
   year = "1977",
   title = "Computational Methods for Data Analysts",
   publisher = "John Wiley and Sons",
   address = "New York",
   kwds = "book, stat, na"
}

@article{chfp:77,
   author = "S. P. Chan and R. Feldman and B. N. Parlett",
   year = "1977",
   title = "Algorithm 517: {A} Program for Computing the Condition
             Numbers of Matrix Eigenvalues Without Computing Eigenvectors",
   journal = "ACM Transactions on Mathematical Software",
   volume = "3",
   pages = "186--203",
   kwds = "nla, eig, pert, condition estimation, software,
           nonsymmetric matrix"
}

@article{chle:79,
   author = "T. F. Chan and J. G. Lewis",
   year = "1979",
   title = "Computing Standard Deviation:  Accuracy",
   journal = "Communications of the ACM",
   volume = "22",
   pages = "536-531",
   kwds = "stat, na, standard deviation, updating"
}

@article{chan:82,
   author = "T. F. Chan",
   year = "1982",
   title = "An Improved Algorithm for Calculating the Singular Value 
             Decomposition",
   journal = "ACM Transactions on Mathematical
               Software",
   volume = "8",
   pages = "72-83",
   kwds = "nla, svd, software"
}

@article{chan:82a,
   author = "T. F. Chan",
   year = "1982",
   title = "Algorithm 581: An Improved Algorithm for Computing the Singular 
	Value Decomposition",
   journal = "ACM Transactions on Mathematical Software",
   volume = "8",
   pages = "84--88",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, svd, software"
}

@techreport{chgl:82,
   author = "T. F. Chan and G. H. Golub and R. J. Le Veque",
   year = "1982",
   title = "Algorithms for Computing the Sample Variance:  Analysis and
             Recommendations",
   institution = "Department of Computer Science, Yale University", 
   number = "222",
   kwds = "stat, na, variance, standard deviation"
}

@article{chke:82,
   author = "T. F. Chan and H. B. Keller",
   year = "1982",
   title = "Arc-Length Continuation and Multi-Grid Techniques for
             Nonlinear Elliptic Eigenvalue Problems",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "3",
   pages = "173--194",
   kwds = "nlop, pde, continuation, elliptic pde"
}

@article{chjz:83,
   author = "T. F. Chan and K. R. Jackson and B. Zhu",
   year = "1983",
   title = "Alternating Direction Incomplete Factorizations",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "20",
   pages = "239--257",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, preconditioning, incomplete factorization"
}

@article{chan:84,
   author = "T. F. Chan",
   year = "1984",
   title = "Deflated Decomposition Solutions of Nearly Singular Systems",
   journal = "{SIAM} Journal on Numerical Analysis",
   volume = "21",
   pages = "738--754",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, deflation, linear system, condition"
}

@article{chan:84a,
   author = "T. F. Chan",
   year = "1984",
   title = "On the Existence and Computation of {LU}-Factorizations
            with Small Pivots",
   journal = "Mathematics of Computation",
   volume = "42",
   pages = "535--547",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, lud, rank determination"
}

@techreport{chre:84,
   author = "T. F. Chan and D. C. Resaco",
   year = "1984",
   title = "On the Condition of Nearly Singular Matrices Under
             Rank-1 Perturbations",
   institution = "Department of Computer Science, Yale University",
   type = "Research Report",
   number = "YALEU/DCS/RR-335",
   kwds = "la, eig, pert, condition"
}

@article{chan:85,
   author = "T. F. Chan",
   year = "1985",
   title = "On the Existence and Computation of {LU} Factorizations with small
            pivots",
   journal = "Mathematics of Computation",
   volume = "42",
   pages = "535--548",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, lud, pivoting"
}

@inproceedings{chan:86,
   author = "T. F. Chan",
   year = "1986",
   title = "Alternative to the {SVD}: Rank Revealing {QR}-Factorizations",
   booktitle = "Proceedings of SPIE---The International Society for
                 Optical Engineering, V.~696.  Advanced Algorithms
                 and Architectures for Signal Processing",
   pages = "31--38",
   publisher = "SPIE",
   address = "Bellingham, Washington",
   kwds = "nla, qrd, condition estimation, rank determination"
}

@article{chan:87,
   author = "T. F. Chan",
   year = "1987",
   title = "Rank Revealing {QR}~Factorizations",
   journal = "Linear Algebra and Its Applications",
   volume = "88/89",
   pages = "67--82",
   kwds = "nla, qrd, condition estimation, rank determination"
}

@article{chan:88,
   author = "T. F. Chan",
   year = "1988",
   title = "An Optimal Circulant Preconditioner for {Toeplitz}
             Systems",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "9",
   pages = "766-771",
   kwds = "nla, linear system, Toeplitz matrix, preconditioning,
           circulant matrix"
}

@book{cgpw:89,
   author = "T. F. Chan and R. Glowinski and J. Periaux
              and O. Widlund, eds.",
   title = "Second International Symposium on Domain Decomposition
             Methods",
   publisher = "SIAM Publications",
   address = "Philadelphia",
   year = "1989",
   kwds = "book, na, domain decomposition, pde"
}

@techreport{chha:89,
   author = "T. F. Chan and P. C. Hansen",
   year = "1990",
   title = "A Stable Extension of {Levinson's} Algorithm for
             Indefinite Toeplitz Systems",
   institution = "Computational and Applied Mathematics,
                   Department of Mathematics, University of
                   California, Los Angeles",
   type = "CAM Report",
   number = "89--20",
   kwds = "nla, Toeplitz matrix, Levinson's algorithm, indefinite system"
}

@article{chha:90,
   author = "T. F. Chan and P. C. Hansen",
   year = "1990",
   title = "Computing Truncated Singular Value Decomposition Least
             Squares Solutions by Rank Revealing {QR}-Factorizations",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "11",
   pages = "519--530",
   kwds = "nla, svd, lsq, rank determination"
}

@unpublished{chha:91,
   author = "T. F. Chan and P. C. Hansen",
   year = "1991",
   title = "Low-Rank Revealing {QR}~Factorizations",
   note = "Manuscript",
   kwds = "nla, qrd, condition, rank determination"
}

@techreport{chha:91a,
   author = "T. F. Chan and P. C. Hansen",
   year = "1991",
   title = "Low-Rank Revealing {QR}~Factorizations",
   institution = "Department of Mathematics, University of
                  California, Los Angeles",
   type = "CAM Report",
   number = "91-08",
   note = "Citation communicated by Per Christian Hansen.",
   kwds = "nla, qrd, pivoting, rank determination"
}

@article{chha:92,
   author = "T. F. Chan and P. C. Hansen",
   year = "1992",
   title = "Some Applications of the Rank Revealing {QR}~Factorization",
   journal = "SIAM Journal on Scientific and Statistical Computing",
   volume = "13",
   pages = "727--741",
   kwds = "nla, qrd, condition, rank determination"
}

@techreport{chip:91,
   author = "S. Chandrasekaran and I. Ipsen",
   year = "1991",
   title = "On Rank-Revealing {QR} Factorizations",
   institution = "Yale University, Department of Computer Science",
   type = "Technical Report",
   number = "YALEU/DCS/RR-880",
   note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
           which is available by anonymous ftp from {\tt math.liu.se} in
           {\tt pub/references}.",
   kwds = "nla, qrd, rank determination"
}

@article{chsa:88,
   author = "H. Y. Chang and M. Salama",
   year = "1988",
   title = "A Parallel {H}ouseholder Tridiagonalization Stratagem
            Using Scattered Square Decomposition",
   journal = "Parallel Computing",
   volume = "6",
   pages = "297--312",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, prll, eig, tridiagonal matrix"
}

@article{chvd:87,
   author = "J. P. Charlier and Van Dooren, P.",
   year = "1987",
   title = "On {K}ogbetliantz's {SVD} Algorithm in the Presence of Clusters",
   journal = "Linear Algebra and its Applications",
   volume = "95",
   pages = "135--160",
   note = "Cited in \cite{govl:89}.",
   kwds = "nla, Kogbetliantz's algorithm, Jacobi-like, svd"
}

@article{chvd:88,
   author = "J. P. Charlier and M. Vangegin and Van Dooren, P.",
   year = "1988",
   title = "On Efficient Implementations of {Kogbetliantz's}
             Algorithm for Computing the Singular
             Value Decomposition",
   journal = "Numerische Mathematik",
   volume = "52",
   pages = "270-300",
   kwds = "nla, svd, Kogbetliantz's algorithm, Jacobi-like"
}

@unpublished{chvd:88a,
   author = "J. P. Charlier and Van Dooren, P.",
   year = "1988",
   title = "A {Jacobi}-Like Algorithm for Computing the
             Generalized {Schur} Form of a Regular Pencil",
   note = "Phillips Research Laboratory, Belgium.",
   kwds = "nla, prll, geig, Jacobi-like"
}

@article{chat:74,
   author = "F. Chatelin-Laborde",
   year = "1974",
   title = "Perturbation d'une matrice hermitienne ou normale",
   journal = "Numerische Mathematik",
   volume = "17",
   pages = "318--337",
   kwds = "la, eig, pert, symmetric matrix, normal matrix"
}

@article{chat:76,
   author = "F. Chatelin-Laborde",
   year = "1976",
   title = "Calcul num\'erique des \'el\'ements propres d'op\'eateurs
             diff\'erentiels int\'egraux par it\'eration",
   journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris, S\'erie A",
   volume = "283",
   pages = "363--365",
   kwds = "nla, eig, functional analysis"
}

@article{chle:78,
   author = "F. Ch