Equidistribution on the Sphere
- 1 March 1997
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 18 (2) , 595-609
- https://doi.org/10.1137/s1064827595281344
Abstract
A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula five kinds of point systems on the sphere, namely lattices in polar coordinates, transformed two-dimensional sequences, rotations on the sphere, triangulations, and "sum of three squares sequence," are investigated. Quantitative tests are done, and the results are compared with one another. Our calculations exhibit different orders of convergence of the generalized discrepancy for different types of point systems.Keywords
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