径向基函数插值中形状参数的选取方法
Selection of Shape Parameters in Radial Basis Function Interpolation
DOI: 10.12677/AAM.2020.99170, PDF,  被引量    国家自然科学基金支持
作者: 王鸿丽*, 龚佃选, 王 玲：华北理工大学理学院，河北 唐山
关键词: 径向基函数；插值精度；形状参数；拉格朗日法；Radial Basis Function； Interpolation Accuracy； Shape Parameter； Lagrange Method
摘要: 径向基函数的形状参数对插值精度的影响很大。如何选取形状参数使得插值误差最小的问题，受到国内外学者的广泛关注。结合径向基函数插值的误差理论，本文围绕形状参数的选取方法进行归纳总结，并通过数值实验，对现有的方法对比研究。为了提高变参数径向基函数的插值精度，提出用拉格朗日法和径向基函数法相结合的方式加以改进。
Abstract: The shape parameters of radial basis function have a great influence on interpolation accuracy. How to select the shape parameters to minimize the interpolation error has been widely concerned by scholars at home and abroad. Combined with the error theory of radial basis function interpolation, the selection methods of shape parameters are summarized in this paper. Through numerical experiments, the existing methods are compared. In order to improve the interpolation accuracy of variable parameter radial basis function, the combination of Lagrange method and radial basis function method is proposed.
文章引用：王鸿丽, 龚佃选, 王玲. 径向基函数插值中形状参数的选取方法[J]. 应用数学进展, 2020, 9(9): 1444-1455. https://doi.org/10.12677/AAM.2020.99170

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