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On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards $ C^s$ functions with $ s>1$


Authors: S. Amat, K. Dadourian and J. Liandrat
Journal: Math. Comp. 80 (2011), 959-971
MSC (2010): Primary 41A05, 41A10, 65D05, 65D17
DOI: https://doi.org/10.1090/S0025-5718-2010-02434-2
Published electronically: November 5, 2010
MathSciNet review: 2772103
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Abstract: 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 Hölder continuous with exponent larger than $ 1.299$. Numerical estimates provide a Hölder 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 Hölder exponent larger than $ 1$.


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Additional Information

S. Amat
Affiliation: Departamento de Matemática Aplicada y Estadística. Universidad Politécnica de Cartagena, Spain
Email: sergio.amat@upct.es

K. Dadourian
Affiliation: Ecole Centrale de Marseille, Laboratoire d’Analyse Topologie et Probabilites, France
Email: dadouria@cmi.univ-mrs.fr

J. Liandrat
Affiliation: Ecole Centrale de Marseille, Laboratoire d’Analyse Topologie et Probabilites, France
Email: jliandrat@centrale-marseille.fr

DOI: https://doi.org/10.1090/S0025-5718-2010-02434-2
Keywords: Nonlinear subdivision scheme, limit function, regularity, stability, Gibbs phenomenon
Received by editor(s): February 18, 2009
Received by editor(s) in revised form: March 20, 2010
Published electronically: November 5, 2010
Additional Notes: The research of the first author was supported in part by the Spanish grants MTM2010-17508 and 08662/PI/08
Article copyright: © Copyright 2010 American Mathematical Society