Fast Verification for Respective Eigenvalues of Symmetric Matrix

  • Shinya Miyajima
  • Takeshi Ogita
  • Shin’ichi Oishi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)


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.


Symmetric Matrix Error Bound Real Symmetric Matrix Approximate Eigenvalue Respective Eigenvalue 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Shinya Miyajima
    • 1
  • Takeshi Ogita
    • 1
    • 2
  • Shin’ichi Oishi
    • 1
  1. 1.Faculty of Science and EngineeringWaseda UniversityShinjuku-ku TokyoJapan
  2. 2.CREST, Japan Science and Technology Agency 

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