Equidistribution on the Sphere

  • 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 2-dimensional sequences, rotations on the sphere, triangulation, and sum of three squares sequence, are investigated. Quantitative tests are done, and the results are compared with each other. Our calculations exhibit different orders of convergence of the generalized discrepancy for different types of point systems.

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Metadaten
Author:Willi Freeden, J. Cui
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5431
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (142)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Source:SIAM J. Sci. Stat. Comput., 18, 595-609 (1997)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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