Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.

Original languageEnglish
Pages (from-to)24-45
Number of pages22
JournalReliable Computing
Volume14
Publication statusPublished - 2010 Jun 1

Keywords

  • Eigenpairs
  • Generalized eigenvalue problem
  • Numerical verification

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

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