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

Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shinichi Oishi

    Research output: Contribution to journalArticle

    12 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

    Fingerprint

    Generalized Eigenvalue Problem
    Eigenvalues and eigenfunctions
    Positive definite
    Theorem
    Quadratic Eigenvalue Problem
    Eigenvector
    Eigenvalue
    Numerical Results

    Keywords

    • Eigenpairs
    • Generalized eigenvalue problem
    • Numerical verification

    ASJC Scopus subject areas

    • Software
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems. / Miyajima, Shinya; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shinichi.

    In: Reliable Computing, Vol. 14, 06.2010, p. 24-45.

    Research output: Contribution to journalArticle

    Miyajima, Shinya ; Ogita, Takeshi ; Rump, Siegfried M. ; Oishi, Shinichi. / Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems. In: Reliable Computing. 2010 ; Vol. 14. pp. 24-45.
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