ON THE ASYMPTOTIC DIRECTIONS OF THE S-DIMENSIONAL OPTIMUM GRADIENT METHOD

Abstract

The optimum s-gradient method for minimizing a positive definite quadratic function f(x) 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 f(x sub 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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Document Details

Document Type
Technical Report
Publication Date
Apr 13, 1967
Accession Number
AD0650619

Entities

People

  • George E. Forsythe

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Chebyshev Polynomials
  • Computer Science
  • Convergence
  • Coordinate Systems
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Inequalities
  • Intervals
  • Iterations
  • Numbers
  • Orthogonality
  • Polynomials
  • Security
  • Sequences
  • Spectra
  • Two Dimensional

Readers

  • Operations Research
  • Statistical inference.