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

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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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 - Plum, Michael

AU - Nakao, Mitsuhiro T.

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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.

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Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

Abstract

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