5 papers · 1 filter
The -Discrepancy with Nonnegative Weights Suffers from the Curse of Dimensionality
Josef Dick
We prove that the -discrepancy with arbitrary nonnegative weights suffers from the curse of dimensionality. More precisely, for every and $d \in \mathb…
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…
Worst-case -approximation of periodic functions using median lattice algorithms
Zexin Pan, Mou Cai, Josef Dick +2
We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space with smoothness in the Lebesgue norm …
The inverse of the star discrepancy of a union of randomly shifted Korobov rank-1 lattice point sets depends polynomially on the dimension
Jiarui Du, Josef Dick
The inverse of the star discrepancy, , defined as the minimum number of points required to achieve a star discrepancy of at most in dimension , is known to depend…
A lattice algorithm with multiple shifts for function approximation in Korobov spaces
Mou Cai, Josef Dick, Takashi Goda
In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in la…