58 citations · 157 across the 61 of their papers we have counts for
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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…
Bernstein approximation and beyond: proofs by means of elementary probability theory
Tiangang Cui, Friedrich Pillichshammer
Bernstein polynomials provide a constructive proof for the Weierstrass approximation theorem, which states that every continuous function on a closed bounded interval can be unifor…