Perturbation analysis for Hermitian, skew-Hermitian, H-even and H-odd matrix polynomials
Sk. Safique Ahmad, Volker Mehrmann · 2010
We discuss the perturbation analysis for eigenvalues and eigenvectors of structured homogeneous matrix polynomials with Hermitian, skew-Hermitian, H-even and H-odd structure. We construct minimal structured perturbations (structured backward errors) such that an approximate eigenpair is an exact eigenpair of an appropriate perturbed structured matrix polynomial. We present various comparisons with unstructured backward errors and previous error bounds derived for the non-homogeneous case and show that our bounds present a significant improvement.