Polynomial Eigenvalue Problems: Theory, Computation, and Structure

Mackey, D. S. and Mackey, N. and Tisseur, F. (2015) Polynomial Eigenvalue Problems: Theory, Computation, and Structure. In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory. Springer International Publishing, Switzerland, pp. 319-348. ISBN 978-3-319-15259-2

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Abstract

Matrix polynomial eigenproblems arise in many application areas, both directly and as approximations for more general nonlinear eigenproblems. One of the most common strategies for solving a polynomial eigenproblem is via a linearization, which replaces the matrix polynomial by a matrix pencil with the same spectrum, and then computes with the pencil. Many matrix polynomials arising from applications have additional algebraic structure, leading to symmetries in the spectrum that are important for any computational method to respect. Thus it is useful to employ a structured linearization for a matrix polynomial with structure. This essay surveys the progress over the last decade in our understanding of linearizations and their construction, both with and without structure, and the impact this has had on numerical practice.

Item Type: Book Section
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Fran├žoise Tisseur
Date Deposited: 12 May 2015
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2293

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