Variation diminishing properties of Bernstein polynomials on a tetrahedron
type: Item
instance of: scholarly article
title: Variation diminishing properties of Bernstein polynomials on a tetrahedron
zbMATH Open document ID: 0814.41020
author: V. Pereyra
published in: Journal of Approximation Theory
publication date: 1994-12-11T00:00:00Z
review text: The authors extend to \(\mathbb{R}^ d\) various definitions of the notions of total variation of a function \(f\) defined on a simplex. The original definitions were given by \textit{T. N. T. Goodman} for functions defined on a triangle [see J. Approximation Theory 50, 111-126 (1987; Zbl 0618.41007) and Constructive Approximation 3, 297-305 (1987; Zbl 0634.41020)]. Estimates are given on the total variation of the \(n\)-th Bernstein polynomial \(B_ n(f)\), of the function by means of the total variation of the \(n\)th Bézier net \(f_ n\) associated with the function. The constants depend on \(n\) and \(d\) and are given explicitly. These estimates extend those obtained by Goodman in the above mentioned papers.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 701328
reviewed by: D. Leviatan
MaRDI profile type: Publication
full work available at URL: jath.1994.1123
OpenAlex ID: W2065878168
DOI: 10.1006/JATH.1994.1123
description: scientific article; zbMATH DE number 701328