ON A NONLINEAR SUBDIVISION SCHEME AVOIDING GIBBS OSCILLATIONS AND CONVERGING TOWARDS Cs FUNCTIONS WITH s > 1

被引：13
作者：
Amat, S. [1 ]
Dadourian, K. [2 ]
Liandrat, J. [2 ]
机构：
[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain
[2] Ecole Cent Marseille, Lab Anal Topol & Probabil, Marseille, France
来源：
MATHEMATICS OF COMPUTATION | 2011年 / 80卷 / 274期
关键词：
Nonlinear subdivision scheme; limit function; regularity; stability; Gibbs phenomenon; MEDIAN-INTERPOLATION; MULTIRESOLUTION; REPRESENTATION;
D O I：
10.1090/S0025-5718-2010-02434-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents a new nonlinear dyadic subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this scheme converges towards limit functions Holder continuous with exponent larger than 1.299. Numerical estimates provide a Holder exponent of 2.438. This subdivision scheme is the first one that simultaneously achieves the control of the Gibbs phenomenon and has limit functions with Holder exponent larger than 1.
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收藏
页码：959 / 971
页数：13
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