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Conference Papers Year : 2015

Tropical diagonal scaling for asymptotic eigenvalue problems

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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Dates and versions

hal-01253175 , version 1 (08-01-2016)

Identifiers

  • HAL Id : hal-01253175 , version 1

Cite

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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