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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.
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https://hal.inria.fr/hal-00782790
Contributor : Canimogy Cogoulane <>
Submitted on : Wednesday, January 30, 2013 - 3:53:48 PM
Last modification on : Thursday, July 8, 2021 - 3:48:14 AM

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  • HAL Id : hal-00782790, version 1

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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. ⟨hal-00782790⟩

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