Tropical bounds for the eigenvalues of structured matrices

Marianne Akian 1, 2 Stéphane Gaubert 1, 2 M. Sharify 3, 4
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
4 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : We establish several inequalities of log-majorization type, relating the moduli of the eigenvalues of a complex matrix or matrix polynomial with the tropical eigenvalues of auxiliary matrix polynomials. This provides bounds which can be computed by combinatorial means. We consider in particular structured matrices and obtain bounds depending on the norms of block submatrices and on the pattern (graph structure) of the matrix.
Type de document :
Communication dans un congrès
2012 SIAM Conference on Applied Linear Algebra, 2012, Valencia, Spain, Spain. 2012
Liste complète des métadonnées

https://hal.inria.fr/hal-00782790
Contributeur : Canimogy Cogoulane <>
Soumis le : mercredi 30 janvier 2013 - 15:53:48
Dernière modification le : mercredi 14 novembre 2018 - 15:20:11

Identifiants

  • HAL Id : hal-00782790, version 1

Citation

Marianne Akian, Stéphane Gaubert, M. Sharify. Tropical bounds for the eigenvalues of structured matrices. 2012 SIAM Conference on Applied Linear Algebra, 2012, Valencia, Spain, Spain. 2012. 〈hal-00782790〉

Partager

Métriques

Consultations de la notice

292