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Formes normales de perturbations de matrices : étude et calcul exact

Abstract : This thesis deals with rational normal forms of matrix perturbations and the eigenvalue perturbation problem : the asymptotic behavior of perturbed eigenvalues only depends on a few monomials of the characteristic polynomial and the goal is thus to be able to "recover" these monomials directly from the initial matrix (quasi-generic perturbations) or at least from a similar matrix perturbation (reduced form). Following Moser and Lidskii, we define two reduced forms that are associated with two different families of quasi-generic matrix perturbations. We also extend Lidskii's perturbation theorem in order to give a third reduced form and to provide a complete solution to the problem. Additionally, a Newton diagram interpretation is detailed for each of these results and some Maple functionalities for handling matrix perturbations are described.
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Contributor : Thèses Imag <>
Submitted on : Tuesday, August 24, 2004 - 4:59:09 PM
Last modification on : Friday, November 6, 2020 - 4:09:31 AM
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  • HAL Id : tel-00006747, version 1



Claude-Pierre Jeannerod. Formes normales de perturbations de matrices : étude et calcul exact. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2000. Français. ⟨tel-00006747⟩



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