Hokkaido Mathematical Journal

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

Tetsuya SAKURAI and Hiroto TADANO

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 3 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1272848031

Digital Object Identifier
doi:10.14492/hokmj/1272848031

Mathematical Reviews number (MathSciNet)
MR2378289

Zentralblatt MATH identifier
1156.65035

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

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

Citation

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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