53 citations · 640 across the 36 of their papers we have counts for
4 papers · 1 filter
On a multi-dimensional Poissonian pair correlation concept and uniform distribution
Aicke Hinrichs, Lisa Kaltenböck, Gerhard Larcher +2
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher d…
The minimal -dispersion of point sets in high-dimensions
Aicke Hinrichs, Joscha Prochno, Mario Ullrich +1
In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set $\mathscr P_…
The curse of dimensionality for numerical integration on general domains
Aicke Hinrichs, Joscha Prochno, Mario Ullrich
We prove the curse of dimensionality in the worst case setting for multivariate numerical integration for various classes of smooth functions. We prove the results when the domains…
Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces
Christopher Kacwin, Jens Oettershagen, Mario Ullrich +1
In this paper, we deal with several aspects of the universal Frolov cubature method, that is known to achieve optimal asymptotic convergence rates in a broad range of function spac…