An explicit formula for the splitting of multiple eigenvalues for nonlinear eigenvalue problems and connections with the linearization for the delay eigenvalue problem

Wim Michiels 1 Islam Boussaada 2, 3, 4 Silviu-Iulian Niculescu 3, 2
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple eigenvalue with respect to a variation of a parameter to the case of multiple nonsemisimple eigenvalues, thereby providing an explicit expression for the leading coefficients of the Puiseux series of the emanating branches of eigenvalues. Second, for a broad class of delay eigenvalue problems, the connection between the finite- dimensional nonlinear eigenvalue problem and an associated infinite-dimensional linear eigenvalue problem is emphasized in the developed perturbation theory. Finally, in contrast to existing work on analyzing multiple eigenvalues of delay systems, we develop all theory in a matrix framework, i.e., without reduction of a problem to the analysis of a scalar characteristic quasi-polynomial.
Type de document :
Article dans une revue
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (2), pp.599-620. 〈10.1137/16M107774X〉
Liste complète des métadonnées

Littérature citée [25 références]  Voir  Masquer  Télécharger

https://hal-centralesupelec.archives-ouvertes.fr/hal-01558169
Contributeur : Islam Boussaada <>
Soumis le : mercredi 10 janvier 2018 - 08:24:53
Dernière modification le : jeudi 5 avril 2018 - 12:30:14

Fichier

MBN-SIAM-2017.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Wim Michiels, Islam Boussaada, Silviu-Iulian Niculescu. An explicit formula for the splitting of multiple eigenvalues for nonlinear eigenvalue problems and connections with the linearization for the delay eigenvalue problem. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (2), pp.599-620. 〈10.1137/16M107774X〉. 〈hal-01558169〉

Partager

Métriques

Consultations de la notice

274

Téléchargements de fichiers

39