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Normalized B-spline-like representation for low-degree Hermite osculatory interpolation problems

Author

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

Abstract

This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with additional smoothness at the vertices of the initial partition, and of the lowest possible degree. A normalized B-spline-like representation for the considered spline space is provided. In addition, several quasi-interpolation operators based on blossoming and control polynomials have also been developed. Some numerical tests are presented and compared with some recent works to illustrate the performance of the proposed approach.

Suggested Citation

  • Boushabi, M. & Eddargani, S. & Ibáñez, M.J. & Lamnii, A., 2024. "Normalized B-spline-like representation for low-degree Hermite osculatory interpolation problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 98-110.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:98-110
    DOI: 10.1016/j.matcom.2024.05.011
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    References listed on IDEAS

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    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.
    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.
    4. Lamnii, A. & Lamnii, M. & Oumellal, F., 2016. "A new basis for osculatory interpolation problems and applications," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 355-368.
    5. Salah Eddargani & María José Ibáñez & Abdellah Lamnii & Mohamed Lamnii & Domingo Barrera, 2021. "Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations," Mathematics, MDPI, vol. 9(18), pages 1-22, September.
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