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November 2007 CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems
Tetsuya SAKURAI, Hiroto TADANO
Hokkaido Math. J. 36(4): 745-757 (November 2007). DOI: 10.14492/hokmj/1272848031


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.


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Tetsuya SAKURAI. Hiroto TADANO. "CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems." Hokkaido Math. J. 36 (4) 745 - 757, November 2007.


Published: November 2007
First available in Project Euclid: 3 May 2010

zbMATH: 1156.65035
MathSciNet: MR2378289
Digital Object Identifier: 10.14492/hokmj/1272848031

Primary: 65F15
Secondary: 65H10

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

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

Vol.36 • No. 4 • November 2007
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