Generalized discrepancies on the sphere | Zendy

Seri Raffaello | Zendy; Choirat Christine | Zendy

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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)

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