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

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

Research output: Contribution to journalArticle

4 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2002 Oct 1
Externally publishedYes


ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this