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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards $C^s$ functions with $s>1$
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by S. Amat, K. Dadourian and J. Liandrat PDF
Math. Comp. 80 (2011), 959-971 Request permission

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
  • MR Author ID: 328783
  • Email: jliandrat@centrale-marseille.fr
  • 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
  • © Copyright 2010 American Mathematical Society
  • 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
  • MathSciNet review: 2772103