Volume 23, Issue 1
A Product Hybrid GMRES Algorithm for Nonsymmetric Linear Systems

Bao-Jiang Zhong

J. Comp. Math., 23 (2005), pp. 83-92.

Published online: 2005-02

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  • Abstract

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES($m$) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES($m$) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.

  • Keywords

Nonsymmetric linear systems, Iterative methods, GMRES, Hybrid, Harmonic Ritz values, Residual polynomials.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-83, author = {}, title = {A Product Hybrid GMRES Algorithm for Nonsymmetric Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {83--92}, abstract = {

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES($m$) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES($m$) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8798.html} }
TY - JOUR T1 - A Product Hybrid GMRES Algorithm for Nonsymmetric Linear Systems JO - Journal of Computational Mathematics VL - 1 SP - 83 EP - 92 PY - 2005 DA - 2005/02 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8798.html KW - Nonsymmetric linear systems, Iterative methods, GMRES, Hybrid, Harmonic Ritz values, Residual polynomials. AB -

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES($m$) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES($m$) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.

Bao-Jiang Zhong. (1970). A Product Hybrid GMRES Algorithm for Nonsymmetric Linear Systems. Journal of Computational Mathematics. 23 (1). 83-92. doi:
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