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Schur-type methods for solving least squares problems with Toeplitz structure
Univ Minnesota, Dept Comp Sci & Engn, Minneapolis, MN 55455 USA Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0003-2281-856X
2000 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, Vol. 22, no 2, 406-430 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2000. Vol. 22, no 2, 406-430 p.
Keyword [en]
corrected seminormal equations, displacement representation, downdating, Givens transformations, hyperbolic transformations, least squares problems, QR decomposition, Schur algorithm, seminormal equations, Toeplitz matrix, updating
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-49608OAI: diva2:270504
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-08-30

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