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2016.61: Polynomial eigenvalue solver based on tropically scaled Lagrange linearization

2016.61: Marc Van Barel and Francoise Tisseur (2016) Polynomial eigenvalue solver based on tropically scaled Lagrange linearization.

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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 2000 > 65 Numerical analysis
MIMS number:2016.61
Deposited By:Dr Françoise Tisseur
Deposited On:26 December 2016

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