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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
LRI - Laboratoire de Recherche en Informatique, LIFL - Laboratoire d'Informatique Fondamentale de Lille, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
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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Submitted on : Wednesday, January 30, 2013 - 3:53:48 PM
Last modification on : Tuesday, October 25, 2022 - 4:19:11 PM


  • HAL Id : hal-00782790, version 1


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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