Tisseur, Françoise and Dedieu, Jean-Pierre
(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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## 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 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: | Ms Lucy van Russelt |

Date Deposited: | 05 Dec 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/984 |

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