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

by Shayne Waldron

Abstract:

A sharp 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: 41A10, 41A65, 41A80 (primary), 41A05, 41A55, 46E99, 65J05 (secondary)

Length: 8 pages

Comment: Written in TeX

Last updated: 7 May 1997

Status: Appeared in Approximation Theory IX - Vol. 1, pp 339--346, (edited by C. K. Chui and L. L. Schumaker), Vanderbilt University Press, 1998

Availability:

This article is available in: