Bounds on the convergence of Ritz values from Krylov subspaces to interior eigenvalues of Hermitean matrices

Abstract

We consider bounds on the convergence of Ritz values from a sequence of Krylov subspaces to interior eigenvalues of Hermitean matrices. These bounds are useful in regions of low spectral density, for example near voids in the spectrum, as is required in many applications. Our bounds are obtained by considering the usual Kaniel-Paige-Saad formalism applied to the shifted and squared matrix.