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Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions

Author

Listed:
  • Abdelouahed Kouibia

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Pedro González

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Miguel Pasadas

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Bassim Mustafa

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Hossain Oulad Yakhlef

    (FSJES of Tetuan, University Abdelmalek Essaidi, Tetuan 93030, Morocco)

  • Loubna Omri

    (FSJES of Tetuan, University Abdelmalek Essaidi, Tetuan 93030, Morocco)

Abstract

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R 2 , and a comparison with another work is analyzed.

Suggested Citation

  • Abdelouahed Kouibia & Pedro González & Miguel Pasadas & Bassim Mustafa & Hossain Oulad Yakhlef & Loubna Omri, 2024. "Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions," Mathematics, MDPI, vol. 12(16), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2597-:d:1461841
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    References listed on IDEAS

    as
    1. Pedro González-Rodelas & Miguel Pasadas & Abdelouahed Kouibia & Basim Mustafa, 2022. "Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions," Mathematics, MDPI, vol. 10(2), pages 1-15, January.
    2. Kouibia, A. & Pasadas, M., 2014. "Optimization of the parameters of surfaces by interpolating variational bicubic splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 76-89.
    3. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
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