Year: 2005
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JCM-8798
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 83–92
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Nonsymmetric linear systems Iterative methods GMRES Hybrid Harmonic Ritz values Residual polynomials.