Comparison of probabilistic and deterministic point sets on the sphere

Peter Grabner, Tetiana Stepaniuk

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

In this paper we make a comparison between certain probabilistic and deterministic point sets and show that some deterministic constructions (especially spherical t-designs) are better or as good as probabilistic ones like the jittered sampling model. We find asymptotic equalities for the discrete Riesz s-energy of sequences of well separated t-designs on the unit sphere S d⊂R d+1, d≥2. The case d=2 was studied in Hesse (2009) and Hesse and Leopardi (2008). In Bondarenko et al., (2015) it was established that for d≥2, there exists a constant c d, such that for every N>c dt d there exists a well-separated spherical t-design on S d with N points. This paper gives results, based on recent developments that there exists a sequence of well separated spherical t-designs such that t and N are related by N≍t d.

Originalspracheenglisch
Seiten (von - bis)128-143
Seitenumfang16
FachzeitschriftJournal of approximation theory
Jahrgang239
DOIs
PublikationsstatusVeröffentlicht - 2019

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T-designs
Point Sets
Unit Sphere
Equality
Sampling
Energy

Schlagwörter

    ASJC Scopus subject areas

    • Analyse
    • Angewandte Mathematik
    • !!Mathematics(all)
    • Numerische Mathematik

    Dies zitieren

    Comparison of probabilistic and deterministic point sets on the sphere. / Grabner, Peter; Stepaniuk, Tetiana.

    in: Journal of approximation theory, Jahrgang 239, 2019, S. 128-143.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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