Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems

A structured backward error analysis for an approximate eigenpair of structured nonlinear matrix equations with T -palindromic, H-palindromic, T -anti-palindromic, and H-anti-palindromic structures is conducted. We construct a minimal structured perturbation in the Frobenius norm such that an approximate eigenpair becomes an exact eigenpair of an appropriately perturbed nonlinear matrix equation. The present work shows that our general framework extends existing results in the literature on the perturbation theory of matrix polynomials.