Title

Uniformly distributed points on the sphere

Abstract

In this work, we present uniformly distributed sequences on the unit sphere, and we show that this property is equivalent to requiring the sequences to have a low discrepancy. Numerical integration over the sphere is taken as a direct application, and the corresponding errors are estimated. Special care is taken in relating these concepts and properties to those for the euclidean case. Several examples of uniformly distributed sequences of nodes (ensembles) are presented.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.3934/cpaa.2005.4.389

Keywords

Discrepancy, Numerical integration, Uniform sequences

Publication Date

6-1-2005

Journal Title

Communications on Pure and Applied Analysis

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