On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon

S. Amat, A. Choutri, J. Ruiz and S. Zouaoui

Applied Mathematics and Computation, 2018, vol. 320, issue C, 16-26

Abstract: A nonlinear ternary 4-point non-interpolatory subdivision scheme is presented. It is based on a nonlinear perturbation of the 4-point subdivision scheme studied in [16]. The convergence of the scheme and the regularity of the limit function are analyzed. It is shown that the Gibbs phenomenon, that is classical in linear schemes, is eliminated. We also establish the stability of the subdivision scheme, that is not a consequence of its convergence due to its non-linearity. To the best of our knowledge, this is the first ternary non-interpolatory subdivision scheme that can be found in the literature.

Keywords: Nonlinear ternary non-interpolatory subdivision scheme; Regularity; Nonlinear subdivision; Stability; Gibbs phenomenon; Signal processing (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:16-26

DOI: 10.1016/j.amc.2017.08.055

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