AN ALGORITHM FOR FINDING RATIONAL APPROXIMATIONS

Abstract

A rational approximation to a function provides a rapid and convenient way to calculate numerical values of the function to within a predetermined error. The question of how to find rational approximations to given functions is considered. Definitions of terms, a precise statement of what the criterion of best fit is, and statements of some classical results are given. Two closely related iterative methods for finding best rational approximations are defined. A proof of convergence of these methods is given for a special case (in which both methods are the (over) same), and these methods are compared with some others. Some results obtained by one of the iterative methods are presented, together with a brief description of the computer program used to obtain them.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1960
Accession Number
AD0248573

Entities

People

  • H. F. Mattson Jr.

Organizations

  • Air Force Cambridge Research Laboratories

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Coefficients
  • Computations
  • Computer Programs
  • Computers
  • Convergence
  • Equations
  • Experimental Data
  • Government Procurement
  • Governments
  • Military Research
  • Polynomials
  • Rational Functions
  • Sequences
  • United States

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)