Uniformly distributed points on the sphere

Jorge Rebaza

doi:10.3934/cpaa.2005.4.389

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2005, Volume 4, Issue 2: 389-403. Doi: 10.3934/cpaa.2005.4.389

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Uniformly distributed points on the sphere

Jorge Rebaza^1,

1.
Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804

Received: March 2004

Revised: December 2004

Published: June 2005

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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.

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Mathematics Subject Classification: 65D30,33C55.

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