## 2006.38: Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

2006.38:
D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann
(2006)
*Structured Polynomial Eigenvalue Problems:
Good Vibrations from Good Linearizations.*
SIAM J. Matrix Anal. Appl., 28 (4).
pp. 1029-1051.
ISSN 0895-4798

*This is the latest version of this eprint.*

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DOI: 10.1137/050628362

## 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 |
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Uncontrolled Keywords: | nonlinear eigenvalue problem, palindromic matrix polynomial, even matrix polynomial, odd matrix polynomial, Cayley transformation, structured linearization, preservation of eigenvalue symmetry |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.38 |

Deposited By: | Nick Higham |

Deposited On: | 19 December 2006 |

### Available Versions of this Item

- Structured Polynomial Eigenvalue Problems:
Good Vibrations from Good Linearizations (deposited 19 December 2006)
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