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 2012Show all

3 papers · 1 filter

math.NA2012★ 97 cited

QMC designs: optimal order Quasi Monte Carlo Integration schemes on the sphere

Johann S. Brauchart, Edward B. Saff, Ian H. Sloan +1

We study equal weight numerical integration, or Quasi Monte Carlo (QMC) rules, for functions in a Sobolev space $H^{s} (S^{d})$ with smoothness parameter $s > d /2$ defined over the unit s…

math.NA2012★ 29 cited

A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness

J. Brauchart, J. Dick

In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $S^{d} \subset R^{d + 1}$ . The reproducing kernel is given by an integr…

math-ph2012★ 47 cited

The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

J. S. Brauchart, D. P. Hardin, E. B. Saff

We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$ -energy of $N$ points on the…