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research
Localization theorems for nonlinear eigenvalue problems
Authors
David Bindel
Amanda Hood
Publication date
4 August 2013
Publisher
Doi
Cite
View
on
arXiv
Abstract
Let
T : \Omega \rightarrow \bbC^{n \times n}
be a matrix-valued function that is analytic on some simply-connected domain
\Omega \subset \bbC
. A point
λ
∈
Ω
\lambda \in \Omega
λ
∈
Ω
is an eigenvalue if the matrix
T
(
λ
)
T(\lambda)
T
(
λ
)
is singular. In this paper, we describe new localization results for nonlinear eigenvalue problems that generalize Gershgorin's theorem, pseudospectral inclusion theorems, and the Bauer-Fike theorem. We use our results to analyze three nonlinear eigenvalue problems: an example from delay differential equations, a problem due to Hadeler, and a quantum resonance computation.Comment: Submitted to SIMAX. 22 pages, 11 figure
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Last time updated on 30/10/2017