J. Brauchart

activity

20072026

most citedDistributing many points on spheres: minimal energy and designs

109 citations · 567 across the 25 of their papers we have counts for

collaborators

Showing 2011 · math.NAShow all

3 papers · 2 filters

math.NA2011★ 36 cited

Point sets on the sphere $S^{2}$ with small spherical cap discrepancy

Christoph Aistleitner, Johann Brauchart, Josef Dick

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discre…

math.NA2011★ 30 cited

A simple Proof of Stolarsky's Invariance Principle

Johann S. Brauchart, Josef Dick

Stolarsky [Proc. Amer. Math. Soc. 41 (1973), 575--582] showed a beautiful relation that balances the sums of distances of points on the unit sphere and their spherical cap $\mathbb…

math.NA2011★ 26 cited

Quasi-Monte Carlo rules for numerical integration over the unit sphere $S^{2}$

Johann S. Brauchart, Josef Dick

We study numerical integration on the unit sphere $S^{2} \subset R^{3}$ using equal weight quadrature rules, where the weights are such that constant functions are in…

Point sets on the sphere S2 with small spherical cap discrepancy

A simple Proof of Stolarsky's Invariance Principle

Quasi-Monte Carlo rules for numerical integration over the unit sphere S2

Point sets on the sphere $S^{2}$ with small spherical cap discrepancy

Quasi-Monte Carlo rules for numerical integration over the unit sphere $S^{2}$