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Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures
Bora, Shreemayee; Karow, Michael; Mehl, Christian; Sharma, Punit
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 a significant difference between the backward errors with respect to structure preserving and arbitrary perturbations in many cases.
Published in: SIAM Journal on Matrix Analysis and Applications, 10.1137/140973839, Society for Industrial and Applied Mathematics
