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A PRODUCT HYBRID GMRES ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS

Baojiang Zhong

Open publisher page 4 citations

Abstract

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may dier 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 ecien t 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 oer signican t performance improvements over the original one.

About this research paper

What this paper is about

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may dier 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 ecien t 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 oer signican t performance improvements over the original one.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may dier 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 ecien t 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 oer signican t performance improvements over the original one.

Key concepts: Generalized minimal residual method, Residual, Linear system, Algorithm, Mathematics, Iterative method, Complement (music), Computer science

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