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.
Original language | English |
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Pages (from-to) | 128-143 |
Number of pages | 16 |
Journal | Journal of approximation theory |
Volume | 239 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Discrete energy
- Energy integral
- Equal-area partition
- Equal-weight numerical integration
- Sphere
- t-design
- The s-energy
- Well-separated point sets
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Mathematics(all)
- Numerical Analysis