ON THE ASYMPTOTIC DIRECTIONS OF THE S-DIMENSIONAL OPTIMUM GRADIENT METHOD
STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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The optimum s-gradient method for minimizing a positive definite quadratic function fx on E sub n has long been known to converge for s or 1. For these s the author studies the directions from which the iterates x sub k approach their limit, and extends to s 1 a theory proved by Akaike for s 1. It is shown that fx sub k can never converge to its minimum value faster than linearly, except in degenerate cases where it attains the minimum in one step.
- Theoretical Mathematics