The Nonlinear Eigenvalue Problem

Güttel, Stefan and Tisseur, Françoise (2017) The Nonlinear Eigenvalue Problem. [MIMS Preprint]

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Abstract

Nonlinear eigenvalue problems arise in a variety of science and engineering applications and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques. Solvers based on Newton's method, contour integration, and sampling via rational interpolation are reviewed. Problems of selecting the appropriate parameters for each of the solver classes are discussed and illustrated with numerical examples. This survey also contains numerous MATLAB code snippets that can be used for interactive exploration of the discussed methods.

Item Type: MIMS Preprint
Uncontrolled Keywords: nonlinear eigenvalue problem, Newton method, contour method, linearization
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 21 Feb 2017
Last Modified: 20 Oct 2017 14:13
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2531

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