A note on backward perturbations for the Hermitian eigenvalue problem
The paper studies two kinds of optimal Hermitian backward perturbations for the Hermitian eigenvalue problem which are obtained from different orthogonal decompositions of computed eigenvectors. It is shown that small residuals and almost orthogonality of the computed eigenvectors does not necessarily imply the smallness of all those optimal perturbations. This contradicts a result by \textit{S. Chandrasekharan} and \textit{I. C. F. Ipsen} [Numer. Math. 68, No. 2, 215-223 (1994; Zbl 0807.65034)] for the real symmetric eigenvalue problem.
optimal Hermitian backward perturbations
scientific article; zbMATH DE number 827433