53 citations · 640 across the 36 of their papers we have counts for
5 papers · 1 filter
Complexity of Oscillatory Integrals on the Real Line
Erich Novak, Mario Ullrich, Henryk Woźniakowski +1
We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space and from the space with a…
Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube
Van Kien Nguyen, Mario Ullrich, Tino Ullrich
In a recent article by two of the present authors it turned out that Frolov's cubature formulae are optimal and universal for various settings (Besov-Triebel-Lizorkin spaces) of fu…
A lower bound for the dispersion on the torus
Mario Ullrich
We consider the volume of the largest axis-parallel box in the -dimensional torus that contains no point of a given point set with elements. We prove that, f…
Comparison of hit-and-run, slice sampling and random walk Metropolis
Daniel Rudolf, Mario Ullrich
Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hyb…
The role of Frolov's cubature formula for functions with bounded mixed derivative
Mario Ullrich, Tino Ullrich
We prove upper bounds on the order of convergence of Frolov's cubature formula for numerical integration in function spaces of dominating mixed smoothness on the unit cube with hom…