Spherical basis functions and uniform distribution of points on spheres

Authors:
Xingping Sun;Zhenzhong Chen
Affiliations:
Institute of Mathematical Sciences, Henan Normal University, Xinxiang, Henan Province, China;Xinxiang College, Xinxiang, Henan Province, China
Venue:
Journal of Approximation Theory
Year:
2008

Citing 16
Cited 1

Real and complex analysis, 3rd ed.

Real and complex analysis, 3rd ed.
Norms of inverses and condition numbers for matrices associated with scattered data

Journal of Approximation Theory
Norm estimates for the inverse of a general class of scattered-data radial-function interpolation matrices

Journal of Approximation Theory
Norm estimates for inverses of Euclidean distance matrices

Journal of Approximation Theory
Conditionally positive definite functions and their application to multivariate interpolations

Journal of Approximation Theory
Conditionally positive definite functions and Laplace-Stieltjes integrals

Journal of Approximation Theory
Inverse and saturation theorems for radial basis function interpolation

Mathematics of Computation
On the optimality of the random hyperplane rounding technique for max cut

Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Energy functionals, numerical integration and asymptotic equidistribution on the sphere

Journal of Complexity
Approximation in rough native spaces by shifts of smooth kernels on spheres

Journal of Approximation Theory
Radial basis functions and corresponding zonal series expansions on the sphere

Journal of Approximation Theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Optimal lower bounds for cubature error on the sphere S2

Journal of Complexity
A lower bound for the worst-case cubature error on spheres of arbitrary dimension

Numerische Mathematik
Cubature over the sphere S2 in Sobolev spaces of arbitrary order

Journal of Approximation Theory
Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions

Foundations of Computational Mathematics

Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration

International Journal of Robotics Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.