  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.
