Tropical diagonal scaling for asymptotic eigenvalue problems

Andrea Marchesini 1, 2
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We study the behaviour of the eigenvalues of a parametric matrix polynomial P in a neighbourhood of zero. If we suppose that the entries of P have Puiseux series expansion, we can build an auxiliary matrix polynomial Q whose entries are the leading exponents of those of P. We show that preconditioning P via a diagonal scaling based on the tropical eigenvalues of Q can improve conditioning and backward error of the eigenvalues.
Type de document :
Communication dans un congrès
The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Aug 2015, Beijing, China. 〈http://www.iciam2015.cn/index.html〉
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https://hal.inria.fr/hal-01253175
Contributeur : Marianne Akian <>
Soumis le : vendredi 8 janvier 2016 - 17:46:11
Dernière modification le : jeudi 10 mai 2018 - 02:05:36

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  • HAL Id : hal-01253175, version 1

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Andrea Marchesini. Tropical diagonal scaling for asymptotic eigenvalue problems. The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Aug 2015, Beijing, China. 〈http://www.iciam2015.cn/index.html〉. 〈hal-01253175〉

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