Polynomial reproduction of vector subdivision schemes
type: Item
instance of: scholarly article
title: Polynomial reproduction of vector subdivision schemes
zbMATH Open document ID: 1470.41010
DOI: 10.1155/2014/104840
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We discuss the polynomial reproduction of vector subdivision schemes with general integer dilation \(m \geq 2\). We first present a simple algebraic condition for polynomial reproduction of such schemes with standard subdivision symbol. We then extend it to general subdivision symbol satisfying certain order of sum rules. We also illustrate our results with several examples. Our results show that such kind of scheme can produce exactly the same scalar polynomial from which the data is sampled by convolving with a finite nonzero sequence of vectors.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 7021744
Wikidata QID: Q59035235
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/104840
OpenAlex ID: W2116229535
cites work: Stationary subdivision
cites work: Subdivision schemes in geometric modelling
cites work: Interpolatory rank-1 vector subdivision schemes
cites work: Polynomial reproduction in subdivision
cites work: Vector cascade algorithms and refinable function vectors in Sobolev spaces
cites work: Q4449255
cites work: Approximation order provided by refinable function vectors
cites work: A family of subdivision schemes with cubic precision
cites work: Polynomial reproduction by symmetric subdivision schemes
cites work: Polynomial reproduction for univariate subdivision schemes of any arity
cites work: Polynomial reproduction of multivariate scalar subdivision schemes
cites work: Vector subdivision schemes in \((L_p(\mathbb R^s))^r\) (\(1\leq p\leq\infty\)) spaces
cites work: Convergence of vector subdivision schemes in Sobolev spaces
cites work: Multiwavelet frames from refinable function vectors
cites work: A study of orthonormal multi-wavelets
cites work: Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets
description: scientific article; zbMATH DE number 7021744