BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-67-61
       ENTRY:: January 03, 1996
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: On the asymptotic directions of the s-dimensional optimum
               gradient method
        TYPE:: Technical Report
      AUTHOR:: Forsythe, George E.
        DATE:: April 1967
       PAGES:: 45
    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.
       NOTES:: [Adminitrivia V1/Prg/19960103]
         END:: STAN//CS-TR-67-61