TY - GEN A1 - Shreemayee, Bora A1 - Michael, Karow A1 - Christian, Mehl A1 - Punit, Sharma T1 - Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures N2 - We derive a formula for the backward error of a complex number $\lambda$ when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. The same are also obtained for approximate eigenvalues of matrix pencils and polynomials with related structures like skew-Hermitian, $*$-even and $*$-odd. Numerical experiments suggest that in many cases there is a significant difference between the backward errors with respect to perturbations that preserve structure and those with respect to arbitrary perturbations. Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1235 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12351 ER -