Bora, ShreemayeeKarow, MichaelMehl, ChristianSharma, Punit2017-12-142017-12-142014-04-170895-4798https://depositonce.tu-berlin.de/handle/11303/7279http://dx.doi.org/10.14279/depositonce-6552We derive a formula for the backward error of a complex number λ 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.en512 Algebra518 Numerische AnalysisHermitian matrix pencilperturbation theoryeigenvalue backward errorstructured mapping problemHermitian matrix polynomialStructured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structuresArticle1095-7162