Optimal perturbation bounds for the Hermitian eigenvalue problem (Q1976906)

This paper looks for optimal error bounds for the relative error of the eigenvalues of \(Hx = \lambda Mx\) for Hermitian matrices \(H\) and \(M\). It extends the theory to the singular case for the generalized eigenvalues that are neither zero nor infinite under the perturbation. The given bounds are optimal, they reflect the structure of the perturbations, and they usually tighten the corresponding global error and conditioning estimates.