138 citations · 788 across the 67 of their papers we have counts for
12 papers · 1 filter
Numerical integration in -Korobov and -cosine spaces
Josef Dick, Peter Kritzer, Gunther Leobacher +1
QMC rules are equal weight quadrature rules for approximating integrals over . One line of research studies the integration error of functions in the unit ball of so-calle…
Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification
Josef Dick, Quoc Thong Le Gia, Christoph Schwab
We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, pa…
Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations
Josef Dick, Quoc T. Le Gia, Christoph Schwab
We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncert…
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling
Johann S. Brauchart, Josef Dick, Lou Fang
In this paper we introduce a reproducing kernel Hilbert space defined on as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}…
Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs
Houying Zhu, Josef Dick
In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we…
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers
Josef Dick, Friedrich Pillichshammer
The inverse of the star-discrepancy problem asks for point sets of size in the -dimensional unit cube whose star-discrepancy satisfies…