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

Author

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

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.

Suggested Citation

  • Amat, S. & Choutri, A. & Ruiz, J. & Zouaoui, S., 2018. "On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 16-26.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:16-26
    DOI: 10.1016/j.amc.2017.08.055
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    References listed on IDEAS

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    1. Rehan, Kashif & Siddiqi, Shahid S., 2015. "A family of ternary subdivision schemes for curves," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 114-123.
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    Cited by:

    1. Mustafa, Ghulam & Hameed, Rabia, 2019. "Families of non-linear subdivision schemes for scattered data fitting and their non-tensor product extensions," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 214-240.

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