Polynomial eigenvalue solver based on tropically scaled Lagrange linearization

Van Barel, Marc and Tisseur, Francoise (2016) Polynomial eigenvalue solver based on tropically scaled Lagrange linearization. [MIMS Preprint]

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Abstract

We propose a novel approach to solve polynomial eigenvalue problems via linearization. The novelty lies in (a) our choice of linearization, which is constructed using input from tropical algebra and the notion of well-separated tropical roots, (b) an appropriate scaling applied to the linearization and (c) a modified stopping criterion for the QZ iterations that takes advantage of the properties of our scaled linearization. Numerical experiments show that our polynomial eigensolver computes all the finite and well-conditioned eigenvalues to high relative accuracy even when they are very different in magnitude.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Fran├žoise Tisseur
Date Deposited: 26 Dec 2016
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2522

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