An Improved Scalar Generated Homotopy Path for Solving f(x) = 0,

Abstract

A new scalar labelling algorithm is presented for solving a system of equations by simplicial approximation. The method presented exhibits strong convergence behavior and supercedes previous simplicial pivot algorithms due to the elimination of an extra dimension, the simplification of the pivoting process by using scalar rather than vector labels, and, most importantly, the nature of the homotopy path taken which has the remarkable properties of monotonicity and Jacobian invariance. Examples are presented wherein the new method converges but Newton's method, Euler's method and previously proposed simplicial pivot algorithms fail to converge. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA034021

Entities

People

  • C. B. Garcia
  • F. J. Gould

Organizations

  • University of Chicago

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Commerce
  • Convergence
  • Elimination
  • Equations
  • Iterations
  • Linear Systems
  • Permutations
  • Schools
  • Sequences
  • Terminals
  • Triangulation

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Graph Algorithms and Convex Optimization.
  • Operations Research