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

Amat, S.; Dadourian, K.; Liandrat, J.

doi:10.1090/S0025-5718-2010-02434-2

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