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February 2009 Generalized Approximate Inverse Preconditioners for Least Squares Problems
Xiaoke Cui, Ken Hayami
Japan J. Indust. Appl. Math. 26(1): 1-14 (February 2009).


This paper is concerned with a new approach for preconditioning large sparse least squares problems. Based on the idea of the approximate inverse preconditioner, which was originally developed for square matrices, we construct a generalized approximate inverse (GAINV) $M$ which approximately minimizes $\|I-MA\|_{\mathrm{F}}$ or $\|I-AM\|_{\mathrm{F}}$. Then, we also discuss the theoretical issues such as the equivalence between the original least squares problem and the preconditioned problem. Finally, numerical experiments on problems from Matrix Market collection and random matrices show that although the preconditioning is expensive, it pays off in certain cases.


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Xiaoke Cui. Ken Hayami. "Generalized Approximate Inverse Preconditioners for Least Squares Problems." Japan J. Indust. Appl. Math. 26 (1) 1 - 14, February 2009.


Published: February 2009
First available in Project Euclid: 5 June 2009

zbMATH: 1171.65390
MathSciNet: MR2518626

Keywords: approximate inverse , least squares problem , matrix , preconditioning , rectangular

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

Vol.26 • No. 1 • February 2009
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