﻿ 径向基函数插值配置点的自适应选取算法 An Adaptive Method for Choosing Collocation Points of RBF Interpolation

Vol.05 No.01(2016), Article ID:16960,7 pages
10.12677/AAM.2016.51002

An Adaptive Method for Choosing Collocation Points of RBF Interpolation

Yu Liu1, Guanglei Liu2, Ziwu Jiang1, Dianxuan Gong3

1School of Sciences, Linyi University, Linyi Shandong

2School of Informatics, Linyi University, Linyi Shandong

3College of Sciences, Hebei Polytechnic University, Tangshan Hebei

Received: Jan. 29th, 2016; accepted: Feb. 19th, 2016; published: Feb. 22nd, 2016

ABSTRACT

Radial basis function (RBF) is one of effective meshfree methods for interpolation on high dimensional scattered data. Since the approximation quality and stability seriously depend on the distribution of the collocation points, it is urgent to find algorithm of choosing optimal point sets for the reconstruction process. In this paper, we give a short overview of existing algorithms including thinning algorithm, greedy algorithm, and so on. A new adaptive data-dependent method is provided at the end with a numerical example to show its efficiency.

1临沂大学理学院，山东 临沂

2临沂大学信息学院，山东 临沂

3河北联合大学理学院，河北 唐山

1. 引言

2. 径向基函数

(1)

(2)

， (3)

3. 配置中心的选取方法

1) 初始步骤：有界区域，在的边界上取一点，令

2) 迭代步骤：对于，在上选取点满足的距离最远，令

4. 我们的选取方法

Figure 1. The profile of the f(x)

Figure 2. The distribution of chosen collocation points

Figure 3. Error function corresponding to 527 equidistant nodes

Figure 4. Error function corresponding to generalized-Leja-Bos sequence of 72 points

5. 数值算例

6. 结论

An Adaptive Method for Choosing Collocation Points of RBF Interpolation[J]. 应用数学进展, 2016, 05(01): 8-14. http://dx.doi.org/10.12677/AAM.2016.51002

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