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2011•Journal of Qiqihar UniversityRequires access

An adaptive preconditioned CRS algorithm

Gao Zhi-zhong

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Abstract

Conjugate residual squared algorithm(CRS) was popular Krylov subspace method for large,sparse and nonsymmetric linear systems.However,the CRS may suffer from irregular convergence,slow convergence or be stationary in some applications.In order to remedy this difficulty,we present an adaptive preconditioner,which is constructed in the iteration step of CRS,by several steps of GMRES(m).Finally,numerical experiments show the effectiveness of the new algorithm.

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What this paper is about

Conjugate residual squared algorithm(CRS) was popular Krylov subspace method for large,sparse and nonsymmetric linear systems.However,the CRS may suffer from irregular convergence,slow convergence or be stationary in some applications.In order to remedy this difficulty,we present an adaptive preconditioner,which is constructed in the iteration step of CRS,by several steps of GMRES(m).Finally,numerical experiments show the effectiveness of the new algorithm.

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Available abstract

Conjugate residual squared algorithm(CRS) was popular Krylov subspace method for large,sparse and nonsymmetric linear systems.However,the CRS may suffer from irregular convergence,slow convergence or be stationary in some applications.In order to remedy this difficulty,we present an adaptive preconditioner,which is constructed in the iteration step of CRS,by several steps of GMRES(m).Finally,numerical experiments show the effectiveness of the new algorithm.

Key concepts: Generalized minimal residual method, Preconditioner, Krylov subspace, Convergence (economics), Conjugate residual method, Residual, Algorithm, Conjugate gradient method

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