Modifications and Alternatives to the Cubic Interpolation Process for One-Dimensional Search.

Abstract

In this paper, the numerical solution of the problem of minimizing a unimodal function f(alpha) is considered, where alpha is a scalar. Two modifications of the cubic interpolation process are presented, so as to improve the robustness of the method and force the process to converge in a reasonable number of iterations. An alternative to the cubic interpolation process is also presented. This is a Lagrange interpolation scheme in which the quadratic approximation to the derivative of the function is considered. The coefficients of the quadratic are determined from the values of the slope at three points: alpha sub 1, alpha sub 2, and alpha sub 3 = (alpha sub 1 + alpha sub 2)/2, where alpha sub 1 and alpha sub 2 are the endpoints of the interval of interpolation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1976
Accession Number
ADA044572

Entities

People

  • Angelo Miele
  • F. Bonardo
  • S. Gonzalez

Organizations

  • Rice University

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  • Abstracts
  • Air Force
  • Algorithms
  • Astronautics
  • Coefficients
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  • Computer Programming
  • Convergence
  • Interpolation
  • Iterations
  • Mathematical Programming
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  • Analytical Mechanics
  • Approximation Theory.