4 papers
A Proof of the Novak--Woźniakowski Conjecture: Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy
Josef Dick
The inverse of the star discrepancy satisfies \[ d \varepsilon^{-1} \lesssim n^{\ast}(d,\varepsilon)\lesssim d\varepsilon^{-2} \] for all $d \in \mathbb{N}…
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…
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…