138 citations · 788 across the 67 of their papers we have counts for
10 papers · 1 filter
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…
Discrepancy bounds for infinite-dimensional order two digital sequences over
Josef Dick
In this paper we provide explicit constructions of digital sequences over the finite field of order 2 in the infinite dimensional unit cube whose first points projected onto th…
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.
Optimal discrepancy bounds for higher order digital sequences over the finite field
Josef Dick, Friedrich Pillichshammer
We show that the discrepancy of the explicitly constructed infinite sequences of points in ove…
A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
J. Brauchart, J. Dick
In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere . The reproducing kernel is given by an integr…
A higher order Blokh-Zyablov propagation rule for higher order nets
Josef Dick, Peter Kritzer
Higher order nets were introduced by Dick as a generalisation of classical -nets, which are point sets frequently used in quasi-Monte Carlo integration algorithms. Essenti…