39 citations · 71 across the 6 of their papers we have counts for
8 papers
Weighted integration over a cube based on digital nets and sequences
Josef Dick, Friedrich Pillichshammer
Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to approximate integrals over the unit cube with respect to the uniform measure. In this paper we discuss QMC inte…
Deep Learning Based Unsupervised and Semi-supervised Classification for Keratoconus
Nicole Hallett, Kai Yi, Josef Dick +4
The transparent cornea is the window of the eye, facilitating the entry of light rays and controlling focusing the movement of the light within the eye. The cornea is critical, con…
A note on the periodic -discrepancy of Korobov's -sets
Josef Dick, Aicke Hinrichs, Friedrich Pillichshammer
We study the periodic -discrepancy of point sets in the -dimensional torus. This discrepancy is intimately connected with the root-mean-square -discrepancy of shifted…
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
Josef Dick, Takashi Goda
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules…
Tractability properties of the discrepancy in Orlicz norms
Josef Dick, Aicke Hinrichs, Friedrich Pillichshammer +1
We show that the minimal discrepancy of a point set in the -dimensional unit cube with respect to Orlicz norms can exhibit both polynomial and weak tractability. In particular,…
Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold
Josef Dick, Martin Ehler, Manuel Gräf +1
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of $\…