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Fast Verification for Respective Eigenvalues of Symmetric Matrix

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Computer Algebra in Scientific Computing (CASC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3718))

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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.

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Author information

Authors and Affiliations

  1. Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku Tokyo, 169-8555, Japan

    Shinya Miyajima, Takeshi Ogita & Shin’ichi Oishi

  2. CREST, Japan Science and Technology Agency,  

    Takeshi Ogita

Authors
  1. Shinya Miyajima
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  2. Takeshi Ogita
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  3. Shin’ichi Oishi
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2005 Springer-Verlag Berlin Heidelberg

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Miyajima, S., Ogita, T., Oishi, S. (2005). Fast Verification for Respective Eigenvalues of Symmetric Matrix. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_26

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  • DOI: https://doi.org/10.1007/11555964_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28966-1

  • Online ISBN: 978-3-540-32070-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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