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Implicit local radial basis function interpolations based on function values

Author

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  • Yao, Guangming
  • Duo, Jia
  • Chen, C.S.
  • Shen, L.H.

Abstract

In this paper we propose two fast localized radial basis function fitting algorithms for solving large-scale scattered data interpolation problems. For each given point in the given data set, a local influence domain containing a small number of nearest neighboring points is established and a global interpolation is performed within this restricted domain. A sparse matrix is formulated based on the global interpolation in these local influence domains. The proposed methods have achieved both low computational cost and minimal memory storage. In comparison with the compactly supported radial basis functions, the proposed fitting algorithms are highly accurate. The numerical examples have provided strong evidence that the two proposed algorithms are indeed highly efficient and accurate. In the two proposed algorithms, we have successfully solved a large-scale interpolation problem with 225,000 interpolation points in two dimensional space.

Suggested Citation

  • Yao, Guangming & Duo, Jia & Chen, C.S. & Shen, L.H., 2015. "Implicit local radial basis function interpolations based on function values," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 91-102.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:91-102
    DOI: 10.1016/j.amc.2015.04.107
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    Citations

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    Cited by:

    1. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. Allasia, Giampietro & Cavoretto, Roberto & De Rossi, Alessandra, 2018. "Hermite–Birkhoff interpolation on scattered data on the sphere and other manifolds," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 35-50.
    3. Assari, Pouria & Asadi-Mehregan, Fatemeh & Cuomo, Salvatore, 2019. "A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 157-172.
    4. Biazar, Jafar & Hosami, Mohammad, 2017. "An interval for the shape parameter in radial basis function approximation," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 131-149.
    5. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.

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