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arXiv · 1303.4668

Localization theorems for nonlinear eigenvalue problems

David Bindel·Amanda Hood
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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 $\lambda \in \Omega$ is an eigenvalue if the matrix $T(\lambda)$ 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.

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David Bindel, Amanda Hood. 2013-03-19. Localization theorems for nonlinear eigenvalue problems. https://arxiv.org/abs/1303.4668

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