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A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation

Author

Listed:
  • Barrera, D.
  • Eddargani, S.
  • Ibáñez, M.J.
  • Lamnii, A.

Abstract

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. With the help of the control polynomial theory introduced herein, a Marsden identity is derived, from which several families of super-convergent quasi-interpolation operators are defined.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:401-415
    DOI: 10.1016/j.matcom.2021.12.003
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    References listed on IDEAS

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    1. 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.
    2. Lamnii, A. & Lamnii, M. & Oumellal, F., 2017. "Computation of Hermite interpolation in terms of B-spline basis using polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 17-27.
    3. 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.
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    Cited by:

    1. Salah Eddargani & Mohammed Oraiche & Abdellah Lamnii & Mohamed Louzar, 2022. "C 2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values," Mathematics, MDPI, vol. 10(9), pages 1-13, April.

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    1. 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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