Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials

Shayne Waldron

Abstract

A <em>sharp</em> pointwise error estimate is given for multivariate
positive linear operators which reproduce the linear polynomials.
This quantitative Korovkin--type theorem generalises a known univariate result.
It is applied to a number of operators including the multivariate
Bernstein operators, and the recently introduced Bernstein--Schoenberg type
operators of Dahmen, Micchelli and Seidel.

Keywords
Korovkin--type theorem, positive linear operator, Bernstein operator, variation diminishing splines, multivariate Bernstein--Schoenberg type operators, radial basis function approximation

Math Review Classification
Primary 41A10, 41A65, 41A80 ; Secondary 41A05, 41A55, 46E99, 65J05

Last Updated
7 May 1997

Length
8 pages

Availability
This article is available in: