Improving certain Bernstein-type approximation processes
This paper deals with a modification of the classical Bernstein polynomials defined on the unit simplex. It introduces a new sequence of non-polynomial linear operators which hold fixed the polynomials x(2) + alpha x and y(2) + beta y with alpha, beta epsilon [0, + infinity). We study the convergence properties of the new approximation process and certain shape properties that are preserved. Finally, we compare it with Bernstein polynomials and show an improvement of the error of convergence in certain subsets of the simplex. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
bivariate bernstein polynomials shape preserving properties error of approximation