On the Asymptotic Directions of the S-dimensional Optimum Gradient Method By

The optimum s-gradient method for minimizing a positive definite quadratic function f(x) on E has long been known to converge for s > 1 . For these £ the author studies the directions from which the iterates x. approach their limit, and extends to s > 1 a theory proved by Akaike for s = 1 . It is shown that f (x. ) 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 Nonr 22^(57) = NR (M 211.