Iterative minimization of the Rayleigh quotient by block steepest descent iterations
Klaus Neymeyr, Ming Quan Zhou · Numerical Linear Algebra with Applications · 2013
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). Copyright © 2013 John Wiley & Sons, Ltd.