Hokkaido Mathematical Journal

SAKURAI Tetsuya, TADANO Hiroto,

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

Hokkaido Mathematical Journal, 36 (2007) pp.745-757

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Abstract

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.

MSC(Primary)65F15
MSC(Secondary)65H10
Uncontrolled Keywordsgeneralized eigenvalue problems, Rayleigh-Ritz procedure, Contour integral, master-worker type algorithm