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C1 Superconvergent quasi-interpolation based on polar forms

Author

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  • Boujraf, A.
  • Tahrichi, M.
  • Tijini, A.

Abstract

In this paper, we use C1 cubic B-splines to construct the Hermite interpolant of any polynomial in terms of their blossom. Consequently, a simple method is presented to get superconvergence phenomenon of cubic spline quasi-interpolants at the knots of a uniform partition. Thanks to this phenomenon, the cubic spline quasi-interpolant provides an interesting approximation very accurate at the superconvergence points. Numerical results are given to illustrate the theoretical ones.

Suggested Citation

  • Boujraf, A. & Tahrichi, M. & Tijini, A., 2015. "C1 Superconvergent quasi-interpolation based on polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 102-115.
    • Handle: RePEc:eee:matcom:v:118:y:2015:i:c:p:102-115
    DOI: 10.1016/j.matcom.2014.12.004
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    References listed on IDEAS

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    1. Foucher, Françoise & Sablonnière, Paul, 2009. "Quadratic spline quasi-interpolants and collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3455-3465.
    2. Abbadi, A. & Ibáñez, M.J. & Sbibih, D., 2011. "Computing quasi-interpolants from the B-form of B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1936-1948.
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    Cited by:

    1. Barrera, D. & Eddargani, S. & Ibáñez, M.J. & Lamnii, A., 2022. "A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 401-415.
    2. Rahouti, A. & Serghini, A. & Tijini, A., 2020. "Construction of superconvergent quasi-interpolants using new normalized C2 cubic B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 603-624.

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