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Conference papers

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
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.
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Submitted on : Friday, January 8, 2016 - 5:46:11 PM
Last modification on : Thursday, January 20, 2022 - 5:27:39 PM


  • HAL Id : hal-01253175, version 1


Andrea Marchesini. Tropical diagonal scaling for asymptotic eigenvalue problems. The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Aug 2015, Beijing, China. ⟨hal-01253175⟩



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