Iterative minimization of the Rayleigh quotient by block steepest descent iterations

The topic of this paper is the convergence analysis of subspace gradient iterations for the simultaneous computation of a few of the smallest eigenvalues plus eigenvectors of a symmetric and positive definite matrix pair (A,M). The methods are based on subspace iterations for A−1M and use the Rayleigh-Ritz procedure for convergence acceleration. New sharp convergence estimates are proved by generalizing estimates which have been presented for vectorial steepest descent iterations (see SIAM J. Matrix Anal. Appl., 32(2):443-456, 2011).