Publication Date



Technical Report: UTEP-CS-11-37


In many applications of interval computations, it turned out to be beneficial to represent polynomials on a given interval [x-, x+] as linear combinations of Bernstein polynomials (x- x - )k * (x+ - x)n-k. In this paper, we provide a theoretical explanation for this empirical success: namely, we show that under reasonable optimality criteria, Bernstein polynomials can be uniquely determined from the requirement that they are optimal combinations of optimal polynomials corresponding to the interval's endpoints.