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. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA106680

Entities

People

  • A. Ben-tal
  • J. Barzilai

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • British Columbia
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Convergence
  • Difference Equations
  • Equations
  • Interpolation
  • Intervals
  • Iterations
  • Linear Systems
  • Nonlinear Systems
  • Polynomials
  • Quadratic Equations
  • Rational Functions

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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
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