Cs 61 . on the Asymptoti S - Dimensional - 0 Pti C Directions of the Mum Gradient Method ' by George

The optimum s-gradient method for minimizing a positive definite quadratic function f(x) on En has long been known to converge for s > 1 . For these s the author studies the directions from which the iterates Xk approach their limit, and extends to s > 1 a theory proved by Akaike for s=l. It is shown that f(xk) can never converge to its minimum value faster than linearly, except in degenerate cases where it attains the minimum in one step. Computer Science Department Stanford University *Research sponsored by the U. S. Office of Naval Research under contract None 225 (37) = NR 044 211.