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June  2005, 4(2): 389-403. doi: 10.3934/cpaa.2005.4.389

Uniformly distributed points on the sphere

Jorge Rebaza 1,

1. 

Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, United States

Received  March 2004 Revised  December 2004 Published  March 2005

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.
Keywords: Uniform sequences, discrepancy, numerical integration.
Mathematics Subject Classification: 65D30,33C55.
Citation: Jorge Rebaza. Uniformly distributed points on the sphere. Communications on Pure and Applied Analysis, 2005, 4 (2) : 389-403. doi: 10.3934/cpaa.2005.4.389
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