Institution: Stanford University, Department of Computer Science

Title: On the asymptotic directions of the s-dimensional optimum gradient method

Author: Forsythe, George E.

Date: April 1967

Abstract: The optimum s-gradient method for minimizing a positive definite quadratic function f(x) on $E_n$ has long been known to converge for s $\geq$ 1. For these $\underline{s}$ the author studies the directions from which the iterates $x_k$ approach their limit, and extends to s > 1 a theory proved by Akaike for s = 1. It is shown that f($x_k$) can never converge to its minimum value faster than linearly, except in degenerate cases where it attains the minimum in one step.

http://i.stanford.edu/pub/cstr/reports/cs/tr/67/61/CS-TR-67-61.pdf