The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis

Details The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis

2011-11-12

arxiv.org/abs/1111.2974v1

Mathematics

Numerical Analysis

in press in Linear Algebra Appl. (2011)

Scientific paper

10.1016/j.laa.2011.10.035

An algorithm based on the Ehrlich-Aberth root-finding method is presented for the computation of the eigenvalues of a T-palindromic matrix polynomial. A structured linearization of the polynomial represented in the Dickson basis is introduced in order to exploit the symmetry of the roots by halving the total number of the required approximations. The rank structure properties of the linearization allow the design of a fast and numerically robust implementation of the root-finding iteration. Numerical experiments that confirm the effectiveness and the robustness of the approach are provided.

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