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math.NA2026
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}…
math.NA2026★ 1 cited
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…
math.NA2025
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…