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 |
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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: | 10 Apr 2017 |
Last Modified: | 20 Oct 2017 14:13 |
URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2538 |
Available Versions of this Item
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The Nonlinear Eigenvalue Problem. (deposited 21 Feb 2017)
- The Nonlinear Eigenvalue Problem. (deposited 10 Apr 2017) [Currently Displayed]
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