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Class D9a4: Other solutions of singular, overdetermined or underdetermined systems of linear equations without constraints

General Information

Parent Class
D9a
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GAMS

Modules

Package CMLIB (Downloadable; Installed on ITL, ARNO)

SUDS
Solves underdetermined systems of linear equations. For full rank matrices the minimum norm solution is returned, as well as an orthonormal basis for the null space of the matrix. If the system of equations is inconsistent only the least squares solution of minimal length is computed.

Package NAPACK (Downloadable)

RSOLVE
Computes the regularized solution to a system of linear equations, given the singular value decomposition of the coefficient matrix.

Package TOMS (Downloadable)

576
MODGE and REFINE: Fortran subroutines for solving an n-by-n system of (possibly singular) linear algebraic equations. The algorithm consists of Gaussian elimination combined with a new pivoting strategy which is particularly well suited to problems where residuals can be made small by solving for fewer than n of the unknowns. (See I. Barrodale and G.F. Stuart, ACM TOMS 7 (1981) pp. 391-397.).

Package VANHUFFEL (Downloadable)

DTLS
Solves, by using a total least squares approximation, the overdetermined system of equations AX=B where both the data matrix A as well as the observation matrix B are inaccurate. This routine will also solve square and underdetermined systems by computing the minimum norm solution. (See S. Van Huffel, J. Comp. Appl. Math. 25 (1989) pp. 111-119.).
PTLS
Uses a total least squares approximation to solve the overdetermined system of equations AX=B where both the data matrix A as well as the observation matrix B are inaccurate. Will also solve square and underdetermined systems by computing the minimum norm solution, and is more efficient than the author''s routine DTLS. (See S. Van Huffel and J. Vandewalle, J. Comp. Appl. Math. 21 (1988), pp. 333-341.).
Comments? gams@nist.gov