Least squares approximation of Bézier coefficients provides best degree reduction in the \(L_2\)-norm
type: Item
instance of: scholarly article
title: Least squares approximation of Bézier coefficients provides best degree reduction in the \(L_2\)-norm
zbMATH Open document ID: 1047.41007
published in: Journal of Approximation Theory
publication date: 2000-01-01T00:00:00Z
review text: Polynomial degree reduction is used to to exchange, and reduce data. In a previous paper the authors and \textit{D. Lutterkort} [Comput. Aided Geom. Design 16, 607--612 (1999; Zbl 0997.65016)] proved that univariante polynomial degree reduction in \(L_2\) equals best Euclidean approximation of Bézier coefficients. This paper extends those results to approximating a multivariate polynomial defined on a simplex by a polynomial of lower degree.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1455759
zbMATH Keywords: polynomials of several variables
zbMATH Keywords: \(d\)-simplex
zbMATH Keywords: degree reduction
Wikidata QID: Q60060309
author: Jörg Peters
author: U. Reif
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
full work available at URL: jath.1999.3443
OpenAlex ID: W2018970480
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DOI: 10.1006/JATH.1999.3443
description: scientific article; zbMATH DE number 1455759