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1995•SIAM Journal on Matrix Analysis and ApplicationsRequires access

A Restarted GMRES Method Augmented with Eigenvectors

Ronald B. Morgan

Open publisher page 308 citations

Abstract

The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace for GMRES. The convergence can be much faster, and the minimum residual property is retained.

About this research paper

What this paper is about

The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace for GMRES. The convergence can be much faster, and the minimum residual property is retained.

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OpenAlex reports 308 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace for GMRES. The convergence can be much faster, and the minimum residual property is retained.

Key concepts: Generalized minimal residual method, Orthogonalization, Eigenvalues and eigenvectors, Mathematics, Krylov subspace, Convergence (economics), Residual, Applied mathematics

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