138 citations · 788 across the 67 of their papers we have counts for
8 papers · 2 filters
Approximation of analytic functions in Korobov spaces
Josef Dick, Peter Kritzer, Friedrich Pillichshammer +1
We study multivariate -approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are d…
Lattice rules for nonperiodic smooth integrands
Josef Dick, Dirk Nuyens, Friedrich Pillichshammer
The aim of this paper is to show that one can achieve convergence rates of for (and for arbitrarily small) for nonperiodic -smooth cosine series usin…
Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher Order Convergence
Josef Dick, Michael Gnewuch
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matc…
On the fast computation of the weight enumerator polynomial and the value of digital nets over finite abelian groups
Josef Dick, Makoto Matsumoto
In this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams type id…
On Wavelet-Galerkin methods for Semilinear Parabolic Equations with Additive Noise
M. Kovács, S. Larsson, K. Urban
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler's method the equation is split into a linear stochastic equation…
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules
Josef Dick
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.