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1996•SIAM Journal on Matrix Analysis and ApplicationsRequires access

A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems

Gérard L. G. Sleijpen, H.A. van der Vorst

Open publisher page 862 citations

Abstract

n this paper we propose a new method for the iterative computation of a few of the extremal. eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi’s approach, combined with Davidson’s method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.

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What this paper is about

n this paper we propose a new method for the iterative computation of a few of the extremal. eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi’s approach, combined with Davidson’s method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.

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OpenAlex reports 862 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

n this paper we propose a new method for the iterative computation of a few of the extremal. eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi’s approach, combined with Davidson’s method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.

Key concepts: Eigenvalues and eigenvectors, Mathematics, Jacobi method, Jacobi eigenvalue algorithm, Computation, Convergence (economics), Applied mathematics, Inverse iteration

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