Fast verification for respective eigenvalues of symmetric matrix

Shinya Miyajima, Takeshi Ogita, Shinichi Oishi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Citations (Scopus)

    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.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Pages306-317
    Number of pages12
    Volume3718 LNCS
    DOIs
    Publication statusPublished - 2005
    Event8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005 - Kalamata
    Duration: 2005 Sep 122005 Sep 16

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume3718 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005
    CityKalamata
    Period05/9/1205/9/16

    Fingerprint

    Symmetric matrix
    Eigenvalue
    Error Bounds
    Eigenvalues of a real symmetric matrix
    Costs and Cost Analysis
    Numerical Examples
    Costs

    ASJC Scopus subject areas

    • Computer Science(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Theoretical Computer Science

    Cite this

    Miyajima, S., Ogita, T., & Oishi, S. (2005). Fast verification for respective eigenvalues of symmetric matrix. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3718 LNCS, pp. 306-317). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3718 LNCS). https://doi.org/10.1007/11555964_26

    Fast verification for respective eigenvalues of symmetric matrix. / Miyajima, Shinya; Ogita, Takeshi; Oishi, Shinichi.

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3718 LNCS 2005. p. 306-317 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3718 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Miyajima, S, Ogita, T & Oishi, S 2005, Fast verification for respective eigenvalues of symmetric matrix. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3718 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3718 LNCS, pp. 306-317, 8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005, Kalamata, 05/9/12. https://doi.org/10.1007/11555964_26
    Miyajima S, Ogita T, Oishi S. Fast verification for respective eigenvalues of symmetric matrix. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3718 LNCS. 2005. p. 306-317. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11555964_26
    Miyajima, Shinya ; Ogita, Takeshi ; Oishi, Shinichi. / Fast verification for respective eigenvalues of symmetric matrix. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3718 LNCS 2005. pp. 306-317 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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