Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems (Q2379363)

The author provides a solution to a question posed by \textit{G. W. Stewart} and \textit{J. Sun} [Matrix perturbation theory. Computer Science and Scientific Computing. Boston etc.: Academic Press, Inc. (1990; Zbl 0706.65013); p. 300] showing that a multiple eigenvalue has different sensitivities under perturbation in a generalized Hermitian eigenvalue problem. An approach providing refined error bounds for a computed multiple eigenvalue after the Rayleigh-Ritz process, introduced previously, is described.