Polynomial reproduction by symmetric subdivision schemes

被引：76

作者：

Dyn, Nira ^{[2
]}

Hormann, Kai ^{[1
]}

Sabin, Malcolm A. ^{[3
]}

Shen, Zuowei ^{[4
]}

机构：

[1] Tech Univ Clausthal, Dept Informat, Clausthal Zellerfeld, Germany

[2] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

[3] Univ Cambridge, Comp Lab, Cambridge CB2 1TN, England

[4] Natl Univ Singapore, Dept Math, Singapore 117548, Singapore

来源：

JOURNAL OF APPROXIMATION THEORY | 2008年 / 155卷 / 01期

关键词：

Subdivision schemes; Polynomial reproduction; Polynomial generation; Approximation order; Quasi-interpolation;

D O I：

10.1016/j.jat.2008.04.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We first present necessary and sufficient conditions for a linear, binary, Uniform, and stationary Subdivision scheme to have polynomial reproduction of degree d and thus approximation order d + 1. Our conditions are partly algebraic and easy to check by considering the symbol of a subdivision scheme, but also relate to the parameterization of the scheme. After discussing some special properties that hold for symmetric schemes, We then use our conditions to derive the maximum degree of polynomial reproduction for two families of symmetric schemes, the family of pseudo-splines and a new family of dual pseudo-splines. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：28 / 42

页数：15

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