Perturbation de valeurs propres de faisceaux matriciels et problème d'affectation optimale

Marianne Akian; Ravindra Bapat; Stéphane Gaubert

doi:10.1016/j.crma.2004.05.001

Perturbation de valeurs propres de faisceaux matriciels et problème d'affectation optimale

Indian Statistical Institute (Delhi Centre)

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Résumé

We extend the perturbation theory of Višik, Ljusternik and Lidskii to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman.

Titre traduit de la contribution	Perturbation of eigenvalues of matrix pencils and the optimal assignment problem
langue originale	Français
Pages (de - à)	103-108
Nombre de pages	6
journal	Comptes Rendus Mathematique
Volume	339
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.crma.2004.05.001
état	Publié - 15 juil. 2004

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10.1016/j.crma.2004.05.001

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title = "Perturbation de valeurs propres de faisceaux matriciels et probl{\`e}me d'affectation optimale",

abstract = "We extend the perturbation theory of Vi{\v s}ik, Ljusternik and Lidskii to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman.",

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N2 - We extend the perturbation theory of Višik, Ljusternik and Lidskii to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman.

AB - We extend the perturbation theory of Višik, Ljusternik and Lidskii to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman.

U2 - 10.1016/j.crma.2004.05.001

DO - 10.1016/j.crma.2004.05.001

M3 - Article

AN - SCOPUS:3042852867

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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Perturbation de valeurs propres de faisceaux matriciels et problème d'affectation optimale

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