Convergence of rational Bernstein operators
Numerical Analysis
2012-06-19 v1
Abstract
In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Pi\c{t}ul and P. Sablonni\`{e}re. It is shown that the rational Bernstein operators R_n converge to the identity operator if and only if \Delta_n, the maximal difference between two consecutive nodes of R_n, is converging to zero. Error estimates in terms of \Delta_n are provided. Moreover a Voronovskaja theorem is presented which is based on the explicit computation of higher order moments for the rational Bernstein operator.
Keywords
Cite
@article{arxiv.1206.4004,
title = {Convergence of rational Bernstein operators},
author = {Hermann Render},
journal= {arXiv preprint arXiv:1206.4004},
year = {2012}
}