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Schur-type methods for solving least squares problems with Toeplitz structure
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DOI：10.1137/S1064827598347423.png)
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We give an overview of fast algorithms for solving least squares problems with Toeplitz structure, based on generalization of the classical Schur algorithm, and discuss their stability properties. In order to obtain more accurate triangular factors of a Toeplitz matrix as well as accurate solutions for the least squares problems, methods based on corrected seminormal equations (CSNE) can be used. We show that the applicability of the generalized Schur algorithm is considerably enhanced when the algorithm is used in conjunction with CSNE. Several numerical tests are reported, where different variants of the generalized Schur algorithm and CSNE are compared for their accuracy and speed.
Keyword:
corrected seminormal equations
displacement representation
downdating
Givens transformations
hyperbolic transformations
least squares problems
QR decomposition
Schur algorithm
seminormal equations
Toeplitz matrix
updating
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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