53 citations · 640 across the 36 of their papers we have counts for
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math.NA2016★ 3 cited
Lattice based integration algorithms: Kronecker sequences and rank-1 lattices
Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki +2
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homo…
math.NA2016★ 28 cited
A Monte Carlo method for integration of multivariate smooth functions
Mario Ullrich
We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set. The main result of this paper is that the mean squared error for a gi…
math.NA2016★ 11 cited
Product rules are optimal for numerical integration in classical smoothness spaces
Aicke Hinrichs, Erich Novak, Mario Ullrich +1
We mainly study numerical integration of real valued functions defined on the -dimensional unit cube with all partial derivatives up to some finite order bounded by one.…