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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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 |
|---|---|
| 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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