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Optimization of the parameters of surfaces by interpolating variational bicubic splines

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  • Kouibia, A.
  • Pasadas, M.

Abstract

In this paper we present an interpolation method from a surface or a data set by the optimization of a quadratic functional in a bicubic splines functional space. The existence and the uniqueness of the solution of this problem are shown and as well a convergence result of the method is established. The mentioned functional involves some real non negative parameters; the optimal surface is obtained by a suitable optimization of these parameters. Finally, we analyze some numerical and graphic examples in order to prove the efficiency of the presented method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:102:y:2014:i:c:p:76-89
    DOI: 10.1016/j.matcom.2013.09.003
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    References listed on IDEAS

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    1. Barrera, D. & Fortes, M.A. & González, P. & Pasadas, M., 2008. "Minimal energy Cr-surfaces on uniform Powell-Sabin type meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 161-169.
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    Cited by:

    1. 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.
    2. Han, Xuli & Han, Jing, 2019. "Bicubic B-spline surfaces constrained by the Biharmonic PDE," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 766-776.

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