Further variation diminishing properties of Bernstein polynomials on triangles
type: Item
instance of: scholarly article
title: Further variation diminishing properties of Bernstein polynomials on triangles
zbMATH Open document ID: 0634.41020
DOI: 10.1007/BF01890572
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: The author gives a new definition of the `variation' of a surface which generalizes those considered previously. See \textit{G. Chang} and \textit{J. Hoschek}, Multivariate Approximation Theory III, Proc. Conf. Oberwolfach/Ger. 1985, ISNM 75, 61-70 (1985; Zbl 0563.41008). It is shown that the variation of a Bernstein polynomial on a triangle is bounded by that of its Dézier net, and conditions are derived under which the bound is attained. A bound is given for the variation of the Bézier net in terms of the variation of the function itself. These results lead to variation diminishing properties of certain approximation operators involving polyhedral splines.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4032290
zbMATH Keywords: variation of a Bernstein polynomial
zbMATH Keywords: Dézier net
zbMATH Keywords: polyhedral splines
author: Tim N. T. Goodman
reviewed by: H. R. Dowson
MaRDI profile type: Publication
cites work: The convexity of Bernstein polynomials over triangles
cites work: Q4735578
cites work: Q3676593
cites work: Q3687145
cites work: Variation diminishing properties of Bernstein polynomials on triangles
full work available at URL: https://doi.org/10.1007/bf01890572
OpenAlex ID: W2032180231
description: scientific article; zbMATH DE number 4032290