Bora, ShreemayeeKarow, MichaelMehl, ChristianSharma, Punit2017-12-142017-12-1420150895-4798https://depositonce.tu-berlin.de/handle/11303/7280http://dx.doi.org/10.14279/depositonce-6553We derive formulas for the backward error of an approximate eigenvalue of a *-palindromic matrix polynomial with respect to *-palindromic perturbations. Such formulas are also obtained for complex T-palindromic pencils and quadratic polynomials. When the T-palindromic polynomial is real, then we derive the backward error of a real number considered as an approximate eigenvalue of the matrix polynomial with respect to real T-palindromic perturbations. In all cases the corresponding minimal structure preserving perturbations are obtained as well. The results are illustrated by numerical experiments. These show that there is a significant difference between the backward errors with respect to structure preserving and arbitrary perturbations in many cases.en518 Numerische Analysis512 Algebrapalindromic matrix pencilpalindromic matrix polynomialperturbation theoryeigenvalue backward errorstructured eigenvalue backward errorArticle1095-7162