Why Bernstein Polynomials: Yet Another Explanation

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-1-2024

Comments

Technical Report: UTEP-CS-24-10

To appear in Proceedings of the NAFIPS International Conference on Fuzzy Systems, Soft Computing, and Explainable AI NAFIPS'2024, South Padre Island, Texas, May 27-29, 2024

Abstract

In many computational situations -- in particular, in computations under interval or fuzzy uncertainty -- it is convenient to approximate a function by a polynomial. Usually, a polynomial is represented by coefficients at its monomials. However, in many cases, it turns out more efficient to represent a general polynomial by using a different basis -- of so-called Bernstein polynomials. In this paper, we provide a new explanation for the computational efficiency of this basis.