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2011•Journal of Hengshui UniversityRequires access

A New Adaptive Preconditioned Global CGS Algorithm

Jing Zhao

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Abstract

Global CGS algorithm(Gl-CGS) is popular matrix Krylov subspace method for large,sparse and nonsymmetric linear systems with multiple right-hand sides.However,the Gl-CGS may suffer from slow convergence or be stationary in some applications.In order to remedy this,we present a new adaptive preconditioner,which is constructed in the iteration.step of Gl-CGS,by several steps of global GMRES(m).Finally,numerical experiments show the effectiveness of the new preconditioner.

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What this paper is about

Global CGS algorithm(Gl-CGS) is popular matrix Krylov subspace method for large,sparse and nonsymmetric linear systems with multiple right-hand sides.However,the Gl-CGS may suffer from slow convergence or be stationary in some applications.In order to remedy this,we present a new adaptive preconditioner,which is constructed in the iteration.step of Gl-CGS,by several steps of global GMRES(m).Finally,numerical experiments show the effectiveness of the new preconditioner.

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Available abstract

Global CGS algorithm(Gl-CGS) is popular matrix Krylov subspace method for large,sparse and nonsymmetric linear systems with multiple right-hand sides.However,the Gl-CGS may suffer from slow convergence or be stationary in some applications.In order to remedy this,we present a new adaptive preconditioner,which is constructed in the iteration.step of Gl-CGS,by several steps of global GMRES(m).Finally,numerical experiments show the effectiveness of the new preconditioner.

Key concepts: Preconditioner, Krylov subspace, Generalized minimal residual method, Convergence (economics), Mathematics, Applied mathematics, Algorithm, Computer science

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