Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators

K. Toyonaga, M. T. Nakao, Y. Watanabe

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    In this paper, we propose a numerical method to verify bounds for multiple eigenvalues for elliptic eigenvalue problems. We calculate error bounds for approximations of multiple eigenvalues and base functions of the corresponding invariant subspaces. For matrix eigenvalue problems, Rump (Linear Algebra Appl. 324 (2001) 209) recently proposed a validated numerical method to compute multiple eigenvalues. In this paper, we extend his formulation to elliptic eigenvalue problems, combining it with a method developed by one of the authors (Jpn. J. Indust. Appl. Math. 16 (1998) 307).

    Original languageEnglish
    Pages (from-to)175-190
    Number of pages16
    JournalJournal of Computational and Applied Mathematics
    Volume147
    Issue number1
    DOIs
    Publication statusPublished - Oct 1 2002

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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