Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

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

doi:10.1137/120894683

Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

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

Research output: Contribution to journal › Article › peer-review

13 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 language	English
Pages (from-to)	975-992
Number of pages	18
Journal	SIAM Journal on Numerical Analysis
Volume	52
Issue number	2
DOIs	https://doi.org/10.1137/120894683
Publication status	Published - 2014
Externally published	Yes

Keywords

Computer-assisted proof
Differential operators
Eigenvalue excluding
Eigenvalue problems

ASJC Scopus subject areas

Numerical Analysis

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10.1137/120894683

Cite this

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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.",

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AU - Nagatou, Kaori

AU - Plum, Michael

AU - Nakao, Mitsuhiro T.

PY - 2014

Y1 - 2014

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AB - 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.

KW - Computer-assisted proof

KW - Differential operators

KW - Eigenvalue excluding

KW - Eigenvalue problems

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Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

Abstract

Keywords

ASJC Scopus subject areas

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