39 citations · 71 across the 6 of their papers we have counts for
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math.NA2019
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
Josef Dick, Takashi Goda
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules…
math.NA2019★ 2 cited
Tractability properties of the discrepancy in Orlicz norms
Josef Dick, Aicke Hinrichs, Friedrich Pillichshammer +1
We show that the minimal discrepancy of a point set in the -dimensional unit cube with respect to Orlicz norms can exhibit both polynomial and weak tractability. In particular,…
math.NA2019
Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold
Josef Dick, Martin Ehler, Manuel Gräf +1
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of $\…