Spherical basis functions and uniform distribution of points on spheres
Spherical basis functions and uniform distribution of points on spheres
复制标题
DOI：
10.1016/j.jat.2007.09.009
复制
发表时间：
2008-04-01
影响因子：
0.9
通讯作者：
Chen, Zhenzhong
中科院分区：
文献类型：
--
作者：
Sun, Xingping;Chen, Zhenzhong
本文的主要目的是利用球面基函数研究球面上点的均匀分布。我们扩展外尔的标准均匀分布的点的领域，包括一个表征的SBF。我们表明，每一组与SBF相关联的最小能量点是均匀分布的领域。给出了基于极小能量点的数值积分的误差估计。我们还估计了最小能量点的分离。(c)2007爱思唯尔公司All rights reserved.
The main purpose of the present paper is to employ spherical basis functions (SBFs) to study uniform distribution of points on spheres. We extend Weyl's criterion for uniform distribution of points on spheres to include a characterization in terms of an SBF. We show that every set of minimal energy points associated with an SBF is uniformly distributed on the spheres. We give an error estimate for numerical integration based on the minimal energy points. We also estimate the separation of the minimal energy points. (c) 2007 Elsevier Inc. All rights reserved.