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An Efficient Variant of the GMRES(m) Method Based on the Error Equations

Published online by Cambridge University Press:  28 May 2015

Akira Imakura ,
Tomohiro Sogabe  and
Shao-Liang Zhang
Akira Imakura*
Affiliation:
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Tomohiro Sogabe
Affiliation:
Aichi Prefectural University, 1522-3 Ibaragabasama, Kumabari, Nagakute-cho, Aichi-gun, Aichi, 480-1198, Japan
Shao-Liang Zhang
Affiliation:
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
*
Corresponding author. Email: a-imakura@na.cse.nagoya-u.ac.jp
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Abstract

The GMRES(m) method proposed by Saad and Schultz is one of the most successful Krylov subspace methods for solving nonsymmetric linear systems. In this paper, we investigate how to update the initial guess to make it converge faster, and in particular propose an efficient variant of the method that exploits an unfixed update. The mathematical background of the unfixed update variant is based on the error equations, and its potential for efficient convergence is explored in some numerical experiments.

Keywords

65F10Nonsymmetric linear systemsGMRES(m) methodrestarterror equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 1 , February 2012 , pp. 19 - 32
Copyright
Copyright © Global-Science Press 2012

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