Publication Date

12-2011

Comments

Technical Report: UTEP-CS-11-62

Abstract

It is well known that an arbitrary continuous function on a bounded set -- e.g., on an interval [a,b] -- can be, with any given accuracy, approximated by a polynomial. Usually, polynomials are described as linear combinations of monomials. It turns out that in many computational problems, it is more efficient to represent a polynomial as Bernstein polynomials -- e.g., for functions of one variable, a linear combination of terms (x-a)k * (b-x)n-k. In this paper, we provide a simple fuzzy-based explanation of why Bernstein polynomials are often more efficient, and we show how this informal explanation can be transformed into a precise mathematical explanation.