TY - GEN A1 - Mehl, Christian T1 - Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures N2 - We 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 significant difference between the backward errors with respect to structure preserving and arbitrary perturbations in many cases. KW - palindromic matrix pencil KW - palindromic matrix polynomial KW - perturbation theory KW - eigenvalue backward error KW - structured eigenvalue backward error Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1306 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13064 ER -