76 citations · 343 across the 42 of their papers we have counts for
5 papers · 2 filters
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…
Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness
Glenn Byrenheid, Lutz Kämmerer, Tino Ullrich +1
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank- integration lattice. The main result is the fact…
Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings
Thomas Kühn, Sebastian Mayer, Tino Ullrich
In this paper, we reveal a new connection between approximation numbers of periodic Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced by a (…
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…
Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions
Aicke Hinrichs, Lev Markhasin, Jens Oettershagen +1
We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces with dominating mixed smoothnes…