6 papers
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…
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…
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…
Lebesgue constants for the Walsh system and the discrepancy of the van der Corput sequence
Josef Dick, Friedrich Pillichshammer
In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue const…