Analysis of the Gibbs phenomenon in stationary subdivision schemes

被引：11

作者：

Amat, Sergio ^{[1
]}

Ruiz, Juan ^{[2
]}

Carlos Trillo, J. ^{[1
]}

Yanez, Dionisio F. ^{[3
,4
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

[2] Univ Alcala, Dept Matemat, Madrid, Spain

[3] Univ Catolica Valencia, Campus Capacitas, Valencia, Spain

[4] Univ Catolica Valencia, CC NN, Dept Matemat, CC SS Aplicadas Educ, Valencia, Spain

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 76卷

关键词：

Binary subdivision; Non-negative masks; B-spline subdivision schemes; Deslauriers-Dubuc subdivision schemes;

D O I：

10.1016/j.aml.2017.08.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper sufficient conditions to determine if a stationary subdivision scheme produces Gibbs oscillations close to discontinuities are presented. It consists of the positivity of the partial sums of the values of the mask. We apply the conditions to non-negative masks and analyze (numerically when the sufficient conditions are not satisfied) the Gibbs phenomenon in classical and recent subdivision schemes like B-splines, Deslauriers and Dubuc interpolation subdivision schemes and the schemes proposed in Siddiqi and Ahmad (2008). (c) 2017 Elsevier Ltd. All rights reserved.

引用

页码：157 / 163

页数：7

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