Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
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DOI：
10.1016/j.camwa.2005.01.010
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发表时间：
2005-01-01
影响因子：
2.9
通讯作者：
Fornberg, B
中科院分区：
文献类型：
--
作者：
Larsson, E;Fornberg, B
本文研究了光滑径向基函数对光滑数据的多元插值问题。从理论上和数值上研究了近平坦径向基函数的插值函数在极限下的性质。给出了不同类型极限的明确准则。利用极限的结果，误差对径向基函数的形状参数的依赖性进行了研究。研究了确定最佳形状参数值的机制，并通过插值误差的近似展开进行了解释。(C)2005爱思唯尔有限公司保留所有权利。
Multivariate interpolation of smooth data using smooth radial basis functions is considered. The behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically. Explicit criteria for different types of limits are given. Using the results for the limits, the dependence of the error on the shape parameter of the radial basis function is investigated. The mechanisms that determine the optimal shape parameter value are studied and explained through approximate expansions of the interpolation error. (C) 2005 Elsevier Ltd. All rights reserved.