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

Translated title of the contribution: Perturbation of eigenvalues of matrix pencils and the optimal assignment problem

Indian Statistical Institute (Delhi Centre)

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Translated title of the contribution	Perturbation of eigenvalues of matrix pencils and the optimal assignment problem
Original language	French
Pages (from-to)	103-108
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	339
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2004.05.001
Publication status	Published - 15 Jul 2004

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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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AU - Akian, Marianne

AU - Bapat, Ravindra

AU - Gaubert, Stéphane

PY - 2004/7/15

Y1 - 2004/7/15

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.

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DO - 10.1016/j.crma.2004.05.001

M3 - Article

AN - SCOPUS:3042852867

SN - 1631-073X

VL - 339

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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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