Lattice rules with random number of points and near $O(n^{-\alpha - 1/2}$ (with Peter Kritzer, Frances Y. Kuo, Dirk Nuyens)

Description

The traditional way to randomize lattice rules is to use a random shift modulo 1, but such a randomization does not improve the convergence rate. We show that by first selecting uniformly a random (prime) number of points $p\tilde U(n/2,n)$ and then drawing uniformly one of the “good” generating vectors for this number of points p, we obtain a randomized worst-case error bound arbitrarily close to $n^-\alpha - 1/2$ where alpha is the smoothness of the usual Korobov space. Moreover, this bound can be made Independent of the number of dimensions by assuming weighted spaces. [1] Peter Kritzer, Frances Y. Kuo, Dirk Nuyens, Mario Ullrich. Lattice rules with random n achieve nearly the optimal O(n^{-\alpha - 1/2) error independently of the dimension. https://arxiv.org/abs/1706.04502, 2017.

Period	02 Jul 2018
Event title	MCQMC 2018, July 1-6 2018, Rennes, France
Event type	Conference
Location	FranceShow on map