8 papers
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 …
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…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part II: digital nets and sequences
Josef Dick, Takashi Goda, Kosuke Suzuki
We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental de…
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…