58 citations · 157 across the 61 of their papers we have counts for
79 papers
The -Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality
Josef Dick, Friedrich Pillichshammer
We study the normalized discrepancy in the Luxemburg norm generated by . For arbitrary nonnegative quadrature weights, we prove that the associated information com…
Infinite sequences with optimal diaphony, periodic -discrepancy, and beyond
Peter Kritzer, Nicolas Nagel, Friedrich Pillichshammer
We investigate the periodic -discrepancy of infinite sequences in and its analytic counterpart, the diaphony. We prove that infinite order-2 digital sequences…
Spherical Cap Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
Johann S. Brauchart, Josef Dick, Friedrich Pillichshammer
We prove that the information complexity (i.e., the inverse) of the classical spherical cap discrepancy on the -dimensional sphere decreases with dimension…
Second order interlaced polynomial lattice rules for integration over
Tiangang Cui, Josef Dick, Friedrich Pillichshammer
We study numerical integration of functions with respect to a probability measure. By applying the corresponding inverse cumulative distribution…
The star discrepancy of a union of randomly digitally shifted Korobov polynomial lattice point sets depends polynomially on the dimension
Josef Dick, Friedrich Pillichshammer
The star discrepancy is a quantitative measure of the uniformity of a point set in the unit cube. A central quantity of interest is the inverse of the star discrepancy, $N(\varepsi…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part I: Lattices and Kronecker sequences
Josef Dick, Takashi Goda, Gerhard Larcher +2
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets…