Fast verification for respective eigenvalues of symmetric matrix

Shinya Miyajima, Takeshi Ogita, Shin'ichi Oishi

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

5 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 publicationComputer Algebra in Scientific Computing - 8th International Workshop, CASC 2005, Proceedings
Pages306-317
Number of pages12
DOIs
Publication statusPublished - 2005 Dec 1
Event8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005 - Kalamata, Greece
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)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005
CountryGreece
CityKalamata
Period05/9/1205/9/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Miyajima, S., Ogita, T., & Oishi, S. (2005). Fast verification for respective eigenvalues of symmetric matrix. In Computer Algebra in Scientific Computing - 8th International Workshop, CASC 2005, Proceedings (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