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

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