Mario Ullrich

activity

20102023

most citedA sharp upper bound for sampling numbers in

L_{2}

53 citations · 640 across the 36 of their papers we have counts for

collaborators

Showing 2017Show all

5 papers · 1 filter

math.NA2017

Digital net properties of a polynomial analogue of Frolov's construction

Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki +2

Frolov's cubature formula on the unit hypercube has been considered important since it attains an optimal rate of convergence for various function spaces. Its integration nodes are…

math.CA2017★ 23 cited

An upper bound on the minimal dispersion

Mario Ullrich, Jan Vybíral

For $ε \in (0, 1/2)$ and a natural number $d \geq 2$ , let $N$ be a natural number with \[ N \,\ge\, 2^9\,\log_2(d)\, \left(\frac{\log_2(1/\varepsilon)}{\varepsilon}\right)^2.…

cs.CG2017★ 14 cited

A note on the dispersion of admissible lattices

Mario Ullrich

In this note we show that the volume of axis-parallel boxes in $R^{d}$ which do not intersect an admissible lattice $L \subset R^{d}$ is uniformly bounded. In…

math.NA2017★ 17 cited

Reproducing Kernels of Sobolev Spaces on $R^{d}$ and Applications to Embedding Constants and Tractability

Erich Novak, Mario Ullrich, Henryk Woźniakowski +1

The standard Sobolev space $W_{2}^{s} (R^{d})$ , with arbitrary positive integers $s$ and $d$ for which $s > d /2$ , has the reproducing kernel $$ K_{d,s}(x,t)=\int_{\mathbb{R}^d}\fra…

math.NA2017★ 19 cited

Lattice rules with random $n$ achieve nearly the optimal $O (n^{- α - 1/2})$ error independently of the dimension

Peter Kritzer, Frances Y. Kuo, Dirk Nuyens +1

We analyze a new random algorithm for numerical integration of $d$ -variate functions over $[0, 1]^{d}$ from a weighted Sobolev space with dominating mixed smoothness $α \geq 0$ and prod…

Digital net properties of a polynomial analogue of Frolov's construction

An upper bound on the minimal dispersion

A note on the dispersion of admissible lattices

Reproducing Kernels of Sobolev Spaces on Rd and Applications to Embedding Constants and Tractability

Lattice rules with random n achieve nearly the optimal O(n−α−1/2) error independently of the dimension

Reproducing Kernels of Sobolev Spaces on $R^{d}$ and Applications to Embedding Constants and Tractability

Lattice rules with random $n$ achieve nearly the optimal $O (n^{- α - 1/2})$ error independently of the dimension