Vassilis Kalantzis
S. 132 - 153
doi:
10.1553/etna_vol52s132
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol52s132
Abstract:
This paper proposes a numerical algorithm based on spectral Schur complements to compute a few eigenvalues and the associated eigenvectors of symmetric matrix pencils. The proposed scheme follows an algebraic domain decomposition viewpoint and transforms the generalized eigenvalue problem into one of computing roots of scalar functions. These scalar functions are defined so that their roots are equal to the eigenvalues of the original pencil, and these roots are computed by Newton's method. We describe the theoretical aspects of the proposed scheme and demonstrate its performance on a few test problems.
spectral Schur complements, domain decomposition, symmetric generalized eigenvalue problem, Newton's method
Published Online:
2020/02/10 12:35:05
Object Identifier:
0xc1aa5576 0x003b48cb
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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