Hokkaido Mathematical Journal

CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems

Tetsuya SAKURAI and Hiroto TADANO

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We consider a Rayleigh-Ritz type eigensolver for finding a limited set of eigenvalues and their corresponding eigenvectors in a certain region of generalized eigenvalue problems. When the matrices are very large, iterative methods are used to generate an invariant subspace that contains the desired eigenvectors. Approximations are extracted from the subspace through a Rayleigh-Ritz projection. In this paper, we present a Rayleigh-Ritz type method with a contour integral (CIRR method). In this method, numerical integration along a circle that contains relatively small number of eigenvalues is used to construct a subspace. Since the process to derive the subspace can be performed in parallel, the presented method is suitable for master-worker programming models. Numerical experiments illustrate the property of the proposed method.

Article information

Hokkaido Math. J. Volume 36, Number 4 (2007), 745-757.

First available in Project Euclid: 3 May 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65F15: Eigenvalues, eigenvectors
Secondary: 65H10: Systems of equations

generalized eigenvalue problems Rayleigh-Ritz procedure Contour integral master-worker type algorithm


SAKURAI, Tetsuya; TADANO, Hiroto. CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems. Hokkaido Math. J. 36 (2007), no. 4, 745--757. doi:10.14492/hokmj/1272848031. https://projecteuclid.org/euclid.hokmj/1272848031

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