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)

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 - 2002 Oct 1
Externally publishedYes

Fingerprint

Multiple Eigenvalues
Elliptic Operator
Numerical Computation
Eigenvalue Problem
Mathematical operators
Numerical methods
Elliptic Problems
Linear algebra
Numerical Methods
Invariant Subspace
Error Bounds
Basis Functions
Verify
Calculate
Formulation
Approximation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators. / Toyonaga, K.; Nakao, M. T.; Watanabe, Y.

In: Journal of Computational and Applied Mathematics, Vol. 147, No. 1, 01.10.2002, p. 175-190.

Research output: Contribution to journalArticle

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