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A fast surrogate cross validation algorithm for meshfree RBF collocation approaches

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  • Marchetti, F.

Abstract

Cross-validation is an important tool in the Radial Basis Function (RBF) collocation setting, especially for the crucial tuning of the shape parameter related to the radial basis function. In this paper, we define a new efficient surrogate cross-validation algorithm, which computes an accurate approximation of the true validation error with much less computational effort with respect to a standard implementation. The proposed scheme is first analyzed and described in detail and then tested in various numerical experiments that confirm its efficiency and effectiveness.

Suggested Citation

  • Marchetti, F., 2024. "A fast surrogate cross validation algorithm for meshfree RBF collocation approaches," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004041
    DOI: 10.1016/j.amc.2024.128943
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    References listed on IDEAS

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    1. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. Karageorghis, Andreas & Tappoura, Demetriana & Chen, C.S., 2021. "The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 581-597.
    3. 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.
    4. Ma, Xiao & Zhou, Bo & Xue, Shifeng, 2021. "A meshless Hermite weighted least-square method for piezoelectric structures," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    5. Chiu, Sung Nok & Ling, Leevan & McCourt, Michael, 2020. "On variable and random shape Gaussian interpolations," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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