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.
Originalsprache | englisch |
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Seiten (von - bis) | 128-143 |
Seitenumfang | 16 |
Fachzeitschrift | Journal of approximation theory |
Jahrgang | 239 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2019 |
ASJC Scopus subject areas
- Analyse
- Angewandte Mathematik
- Mathematik (insg.)
- Numerische Mathematik