Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper presents eigenvalue excluding methods for self-adjoint or non-self-adjoint eigenvalue problems in Hilbert spaces, including problems with partial differential operators. Eigenvalue exclosure means the determination of subsets of the complex field which do not contain eigenvalues of the given problem. Several verified eigenvalue excluding results for ordinary and partial differential operators are reported on.

Original languageEnglish
Pages (from-to)975-992
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Hilbert spaces
Set theory
Eigenvalue Problem
Mathematical operators
Hilbert space
Eigenvalue
Partial Differential Operators
Adjoint Problem
Subset

Keywords

  • Computer-assisted proof
  • Differential operators
  • Eigenvalue excluding
  • Eigenvalue problems

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. / Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.

In: SIAM Journal on Numerical Analysis, Vol. 52, No. 2, 2014, p. 975-992.

Research output: Contribution to journalArticle

Watanabe, Yoshitaka ; Nagatou, Kaori ; Plum, Michael ; Nakao, Mitsuhiro T. / Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. In: SIAM Journal on Numerical Analysis. 2014 ; Vol. 52, No. 2. pp. 975-992.
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