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. 10291051. ISSN 08954798
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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]

Structured Polynomial Eigenvalue Problems:
Good Vibrations from Good Linearizations. (deposited 22 Mar 2006)
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