A note on bivariate box splines on a k-direction mesh
type: Item
instance of: scholarly article
title: A note on bivariate box splines on a k-direction mesh
zbMATH Open document ID: 0602.41013
DOI: 10.1016/0377-0427(86)90244-X
author: B. George
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: For \(k\geq 2\), a k-direction mesh is a set of vectors \(X=\{v^ 1,...,v^ 1,...,v^ k,...,v^ k\},\) with \(m_ 1\)-times \(v^ 1,...\), \(m_ k\)- times \(v^ k\), \(m_ i\geq 1\), where \(v^ i=(\alpha_ i,\beta_ i)\in {\mathbb{Z}}^ 2\), with \(\beta_ i\geq 0\) and \(\alpha_ i\beta_ j\neq \alpha_ j\beta_ i\) for \(i\neq j\). The author shows that the dimension of the polynomial subspace \(S_{\pi}(X)\) of the linear span of translates of bivariate box splines [see for definition \textit{C. de Boor} and \textit{R. DeVore}, Trans. Am. Math. Soc. 276, 775-788 (1983; Zbl 0529.41010)] over lattice points in \({\mathbb{Z}}^ 2\) is given by \(\dim S_{\pi}(X)=\sum_{1\leq i<j\leq k}m_ i m_ j.\)
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3971384
zbMATH Keywords: rate of approximation
zbMATH Keywords: dimension of polynomial subspace
zbMATH Keywords: k-direction mesh
zbMATH Keywords: translates
zbMATH Keywords: bivariate box splines
zbMATH Keywords: lattice points
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
cites work: Approximation by Smooth Multivariate Splines
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cites work: B-splines from parallelepipeds
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cites work: Q5185474
cites work: Some results on box splines
cites work: Translates of multivariate splines
description: scientific article; zbMATH DE number 3971384