Nonpolynomial and Inverse Interpolation for Line Search: Synthesis and Convergence Rates

Abstract

The rate of convergence of line search algorithms based on general interpolating functions is derived, and is shown to be independent of the particular interpolating function used. This result holds for the root finding problem f(x) = 0 as well. We show how inverse interpolation can be used in conjunction with the line search problem, and derive its rate of convergence. Our analysis suggests that one-point line search algorithms (in particular Newton's method) are inefficient in a sense. Two-point algorithms using rational interpolating functions are recommended.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1980
Accession Number
ADA095022

Entities

People

  • A. Ben-tal
  • J. Barzilai

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • British Columbia
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Convergence
  • Difference Equations
  • Equations
  • Iterations
  • Linear Systems
  • Mathematical Programming
  • Polynomials
  • Quadratic Equations
  • Rational Functions
  • Sequences

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Approximation Theory.