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Hungarian Scaling of Polynomial Eigenproblems

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 expansions 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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https://hal.inria.fr/hal-01252398
Contributor : Marianne Akian <>
Submitted on : Thursday, January 7, 2016 - 3:13:15 PM
Last modification on : Friday, April 30, 2021 - 9:56:03 AM

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  • HAL Id : hal-01252398, version 1

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Marianne Akian, Stephane Gaubert, Andrea Marchesini, Françoise Tisseur. Hungarian Scaling of Polynomial Eigenproblems . SIAM Conference on Applied Linear Algebra (SIAM LA), Oct 2015, Atlanta, United States. ⟨hal-01252398⟩

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