APPROXIMATION OF EMPIRICAL FUNCTIONS OF DISCRETE DISTRIBUTION BY DISCONTINUOUS ORTHOGONAL POLYNOMIALS,

Abstract

Compensation of empirical functions by whole rational functions according to the Gaussian method of least squares leads to systems of linear equations the solution of which, at large numbers of given functional values, becomes very difficult, and becomes numerically impossible with increasing number of values. Application of orthogonal polynomials developed in this paper eliminates the solution of these systems of equation, and by means of these orthogonal polynomials whole rational functions can be given rapidly which approximate with any desired degree of accuracy the given functional values, and which in the limiting case, yield the exact interpolation. By means of an example (N = 75) application of this method is demonstrated. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 26, 1947
Accession Number
AD0606207

Entities

People

  • Vettin

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Compensation
  • Discrete Distribution
  • Equations
  • Interpolation
  • Mathematics
  • Polynomials
  • Rational Functions

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Systems Analysis and Design