Palindromic Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker (2006) Palindromic Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. [MIMS Preprint]

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Abstract

Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomial (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations that reflect the structure of these polynomials, and therefore preserve symmetries in their spectra, is introduced and investigated. We analyze the existence and uniqueness of such linearizations, and show how they may be systematically constructed.

Item Type: MIMS Preprint
Uncontrolled Keywords: nonlinear eigenvalue problem, palindromic matrix polynomial, even matrix polynomial, odd matrix polynomial, Cayley transformation, structured linearization, preservation of eigenvalue symmetry
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: Nick Higham
Date Deposited: 22 Mar 2006
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/189

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