Fast verification for respective eigenvalues of symmetric matrix

Authors:
Shinya Miyajima;Takeshi Ogita;Shin'ichi Oishi
Affiliations:
Faculty of Science and Engineering, Waseda University, Shinjuku-ku Tokyo, Japan;Faculty of Science and Engineering, Waseda University, Shinjuku-ku Tokyo, Japan;Faculty of Science and Engineering, Waseda University, Shinjuku-ku Tokyo, Japan
Venue:
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Year:
2005

Citing 3
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The symmetric eigenvalue problem

The symmetric eigenvalue problem
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Abstract

A fast verification algorithm of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a small additional cost. Finally, this paper includes some numerical examples to show the efficiency of the proposed algorithm.