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Generalized Linear Least Squares (LSE and GLM) Problems
Driver routines are provided for two types of generalized linear least squares
problems.
The first is

(2.2) 
where A is an mbyn matrix and B is a pbyn matrix,
c is a given mvector, and d is a given pvector,
with
.
This is
called a linear equalityconstrained least squares problem (LSE).
The routine xGGLSE
solves this problem using the generalized RQ
(GRQ) factorization, on the
assumptions that B has full row rank p and
the matrix
has full column rank n.
Under these assumptions, the problem LSE has a unique solution.
The second generalized linear least squares problem is

(2.3) 
where A is an nbym matrix, B is an nbyp matrix,
and d is a given nvector,
with
.
This is sometimes called a general (GaussMarkov) linear model problem (GLM).
When B = I, the problem reduces to an ordinary linear least squares problem.
When B is square and nonsingular, the GLM problem is equivalent to the
weighted linear least squares problem:
The routine xGGGLM
solves this problem using the generalized QR (GQR)
factorization, on the
assumptions that A has full column rank m, and the
matrix ( A, B ) has full row rank n. Under these assumptions, the
problem is always consistent, and there are unique solutions x and y.
The driver routines for generalized linear least squares problems are listed
in Table 2.4.
Table 2.4:
Driver routines for generalized linear least squares problems
Operation 
Single precision 
Double precision 

real 
complex 
real 
complex 
solve LSE problem using GRQ 
SGGLSE 
CGGLSE 
DGGLSE 
ZGGLSE 
solve GLM problem using GQR 
SGGGLM 
CGGGLM 
DGGGLM 
ZGGGLM 
Next: Standard Eigenvalue and Singular
Up: Driver Routines
Previous: Linear Least Squares (LLS)
Contents
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Susan Blackford
19991001