Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker (2006) Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. SIAM J. Matrix Anal. Appl., 28 (4). pp. 1029-1051. ISSN 0895-4798

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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:	Article
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:	19 Dec 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/671

Available Versions of this Item

• Palindromic Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. (deposited 22 Mar 2006)
  • Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. (deposited 22 Mar 2006)
    • Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. (deposited 19 Dec 2006) [Currently Displayed]

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