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On the asymptotic directions of thes-dimensional optimum gradient method

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Abstract

The optimums-gradient method for minimizing a positive definite quadratic functionf(x) onE n has long been known to converge fors ≧+1. For theses the author studies the directions from which the iteratesx k approach their limit, and extends tos>1 a theory proved byAkaike fors=1. It is shown thatf (x k ) can never converge to its minimum value faster than linearly, except in degenerate cases where it attains the minimum in one step.

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Authors and Affiliations

  1. Computer Science Department, Stanford University, 94305, Stanford, California, USA

    George E. Forsythe

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  1. George E. Forsythe
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Dedicated to ProfessorHeinrich Brinkmann for his seventieth birthday.

Research sponsored by the U.S. Office of Naval Research under project NR 044211.

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Forsythe, G.E. On the asymptotic directions of thes-dimensional optimum gradient method. Numer. Math. 11, 57–76 (1968). https://doi.org/10.1007/BF02165472

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