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1994•Numerical Linear Algebra with ApplicationsRequires access

GMRESR: a family of nested GMRES methods

H.A. van der Vorst, C. Vuik

Open publisher page 288 citations

Abstract

Abstract Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU‐time and memory requirements in typical CFD applications.

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What this paper is about

Abstract Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU‐time and memory requirements in typical CFD applications.

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Available abstract

Abstract Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU‐time and memory requirements in typical CFD applications.

Key concepts: Generalized minimal residual method, Preconditioner, Mathematics, Linear system, Iterative method, Applied mathematics, Process (computing), Mathematical optimization

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