Japan Journal of Industrial and Applied Mathematics

Generalized Approximate Inverse Preconditioners for Least Squares Problems

Xiaoke Cui and Ken Hayami

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Abstract

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.

Article information

Source
Japan J. Indust. Appl. Math., Volume 26, Number 1 (2009), 1-14.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1244209203

Mathematical Reviews number (MathSciNet)
MR2518626

Zentralblatt MATH identifier
1171.65390

Keywords
approximate inverse least squares problem preconditioning rectangular matrix

Citation

Cui, Xiaoke; Hayami, Ken. Generalized Approximate Inverse Preconditioners for Least Squares Problems. Japan J. Indust. Appl. Math. 26 (2009), no. 1, 1--14. https://projecteuclid.org/euclid.jjiam/1244209203


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