A constructive enclosure approximation of a continuous function of many variables by piecewise linear functions

Abstract

In this paper, for contributing to solve the problems of one-sided, or two-sided approximation, a constructive enclosure approximation (having representable lower and upper bounds) of a continuous function of many variables by piecewise linear functions is provided. A theorem of a representation like Kolmogorov's superposition theorem of continuous functions of many variables is provided, and a theorem of a constructive piecewise linear enclosure of a continuous function of many variables is also provided. By using an implementation of the theorems on Maple, the examples of piecewise linear enclosures of a polynomial and a transcendental function of three variables are obtained.