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Volume 2, Issue 1
An Efficient Variant of the GMRES(m) Method Based on the Error Equations

Akira Imakura, Tomohiro Sogabe & Shao-Liang Zhang

DOI: 10.4208/eajam.280611.030911a

East Asian J. Appl. Math., 2 (2012), pp. 19-32.

Published online: 2018-02

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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

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

  • AMS Subject Headings

65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-19, author = {Akira Imakura, Tomohiro Sogabe and Shao-Liang Zhang}, title = {An Efficient Variant of the GMRES(m) Method Based on the Error Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280611.030911a}, url = {http://global-sci.org/intro/article_detail/eajam/10864.html} }
TY - JOUR T1 - An Efficient Variant of the GMRES(m) Method Based on the Error Equations AU - Akira Imakura, Tomohiro Sogabe & Shao-Liang Zhang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 19 EP - 32 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.280611.030911a UR - https://global-sci.org/intro/article_detail/eajam/10864.html KW - Nonsymmetric linear systems, GMRES($m$) method, restart, error equations. AB -

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.

Akira Imakura, Tomohiro Sogabe and Shao-Liang Zhang. (2018). An Efficient Variant of the GMRES(m) Method Based on the Error Equations. East Asian Journal on Applied Mathematics. 2 (1). 19-32. doi:10.4208/eajam.280611.030911a
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