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Curve fitting by GLSPIA

Author

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  • Zhuang, Jiayuan
  • Zhu, Yuanpeng
  • Zhong, Jian

Abstract

We develop the generalized B-splines least square progressive iterative approximation (GLSPIA) method to improve LSPIA method (Deng and Lin, 2014) from the perspective of its equivalent neural network framework. We replace the B-spline basis function in standard LSPIA method with the generalized B-spline basis function (Juhász and Róth, 2013) in the GLSPIA method. By adjusting the control points as well as the parameter in the core function, higher precision fitting is achieved. Moreover, in order to solve the over-fitting problem of GLSPIA method when dealing with noise data, we propose three kinds of regularizations using the geometric properties of control polygon. Numerical examples are presented to show the effectiveness of our method.

Suggested Citation

  • Zhuang, Jiayuan & Zhu, Yuanpeng & Zhong, Jian, 2024. "Curve fitting by GLSPIA," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323005969
    DOI: 10.1016/j.amc.2023.128427
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    References listed on IDEAS

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    1. Liu, Chengzhi & Liu, Zhongyun & Han, Xuli, 2021. "Preconditioned progressive iterative approximation for tensor product Bézier patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 372-383.
    2. Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.
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