## 2007.227: Perturbation theory for homogeneous polynomial eigenvalue problems

2007.227:
Françoise Tisseur and Jean-Pierre Dedieu
(2003)
* Perturbation theory for homogeneous polynomial eigenvalue problems.*
Linear Algebra and its Applications, 385 (1).
pp. 71-74.
ISSN 0024-3795

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Postscript - Requires a viewer, such as GSview 322 Kb |

DOI: 10.1016/S0024-3795(01)00423-2

## Abstract

We consider polynomial eigenvalue problems P(A,alpha,beta)x=0 in which the matrix polynomial is homogeneous in the eigenvalue (alpha,beta)&unknown;C2. In this framework infinite eigenvalues are on the same footing as finite eigenvalues. We view the problem in projective spaces to avoid normalization of the eigenpairs. We show that a polynomial eigenvalue problem is well-posed when its eigenvalues are simple. We define the condition numbers of a simple eigenvalue (alpha,beta) and a corresponding eigenvector x and show that the distance to the nearest ill-posed problem is equal to the reciprocal of the condition number of the eigenvector x. We describe a bihomogeneous Newton method for the solution of the homogeneous polynomial eigenvalue problem (homogeneous PEP)

Item Type: | Article |
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Uncontrolled Keywords: | Mathematical Subject Codes] 65F15; [Mathematical Subject Codes] 15A18; Polynomial eigenvalue problem; Matrix polynomial; Quadratic eigenvalue problem; Condition number |

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

MIMS number: | 2007.227 |

Deposited By: | Ms Helen Kirkbright |

Deposited On: | 05 December 2007 |

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