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

摘要: 径向基函数是一种处理高维散乱数据插值的有效方法。由于逼近精度和稳定性都严重依赖于配置点的分布，因此在重建过程中如何设计配置点的优化选取算法成为一个迫切需要解决的问题。在本文中，我们将简要介绍已有的选取算法，例如：细化算法、贪婪算法等。文章的最后，我们给出一种新的自适应选取算法，并通过数值算例验证该方法的高效性。

Abstract: Radial basis function (RBF) is one of effective meshfree methods for interpolation on high dimen-sional scattered data. Since the approximation quality and stability seriously depend on the dis-tribution 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 pro-vided at the end with a numerical example to show its efficiency.