Under the over-promising title the reader finds a compact review
and a few new theorems on the convergence of the smallest
eigenvalues only. Anyhow, nice sharp estimates (which, by
definition, cannot be improved in generic cases) are offered for
the usual factor of the error reduction after one iteration, as
well as for its asymptotic average-upper-limit alternative.


MR2206453 Ovtchinnikov, E. E. Sharp convergence estimates for the
preconditioned steepest descent method for Hermitian eigenvalue
problems. SIAM J. Numer. Anal. 43 (2006), no. 6, 2668--2689
(electronic). 65F15