The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis
This work addresses the need for efficient eigenvalue computation for structured matrix polynomials, offering a specialized method for T-palindromic polynomials.
The paper presents an algorithm based on the Ehrlich-Aberth method to compute eigenvalues of T-palindromic matrix polynomials, using a structured linearization in the Dickson basis to halve the number of required approximations. Numerical experiments confirm effectiveness and robustness.
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.