Uniform rational approximation of functions of several variables

Abstract

AbstractWe present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.