#### Publication Date

12-2011

#### 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.

## Comments

Technical Report: UTEP-CS-11-62