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Generalized discrepancies on the sphere
Author(s) -
Seri Raffaello,
Choirat Christine
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700216
Subject(s) - unit sphere , convergence (economics) , measure (data warehouse) , mathematics , class (philosophy) , unit (ring theory) , mathematical analysis , pure mathematics , computer science , artificial intelligence , mathematics education , database , economics , economic growth
Generalized discrepancies are a class of discrepancies introduced in the seminal paper [1] to measure uniformity of points over the unit sphere in ℝ 3 . However, convergence to 0 of this quantity has been shown only in the case of spherical t –designs. In the following, we completely characterize sequences for which convergence to 0 of D ( N ; A ) holds. The interest of this result is that, when evaluating uniformity on the sphere, generalized discrepancies are much simpler to compute than the well‐known spherical cap discrepancy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)