Improved Interval Bounds for Ranges of Functions.

Abstract

Evaluation of a real function f on an interval X using interval arithmetic yields an interval extension F(X) containing the range R(f;X) of f on X. Unfortunately, F(X) is sometimes excessively wider than R(f;X). Evaluation of f epsilon C1 by interval differentiation arithmetic gives F(X) and the extension F'(X) of f' on X. If F' (X) > 0 (or F'(X) < 0), then f is monotone on X = (a,b), and R(f;X) = (f(a), f(b)) (or R(f;X) = (f(b), f(a))), giving improved bounds for R(f;X). If 0 epsilon int(F'(X)), then X is divided into subintervals on which f is either guaranteed to be monotone or has possible extremal points. A Pascal-SC program for this simple algorithm is given, and numerical results are presented. As a byproduct of the computation, possible extremal points of f are isolated. Keywords: Range of functions; Extremal points; Automatic differentiation; Interval computation; Optimization; Pascal-SC.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA163627

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Automatic
  • Calculus
  • Computations
  • Computer Programs
  • Computers
  • Mathematics
  • Monotone Functions
  • North Carolina
  • Numbers
  • Optimization
  • Procedures (Computers)
  • Real Numbers
  • Test And Evaluation
  • United States
  • Universities

Fields of Study

  • Mathematics

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