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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 m-by-n matrix and B is a p-by-n matrix, c is a given m-vector, and d is a given p-vector, with . This is called a linear equality-constrained 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 n-by-m matrix, B is an n-by-p matrix, and d is a given n-vector, with . This is sometimes called a general (Gauss-Markov) 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.

 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   Index
Susan Blackford
1999-10-01