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

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

Year:    2012

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 19–32

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.280611.030911a

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 19–32

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Nonsymmetric linear systems GMRES($m$) method restart error equations.

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