6 citations · 12 across the 12 of their papers we have counts for
18 papers
Exact order of extreme discrepancy of infinite sequences in arbitrary dimension
Ralph Kritzinger, Friedrich Pillichshammer
We study the extreme discrepancy of infinite sequences in the -dimensional unit cube, which uses arbitrary sub-intervals of the unit cube as test sets. This is in contrast…
Point sets with optimal order of extreme and periodic discrepancy
Ralph Kritzinger, Friedrich Pillichshammer
We study the extreme and the periodic discrepancy of point sets in the -dimensional unit cube. The extreme discrepancy uses arbitrary sub-intervals of the unit cube as tes…
Uniformly distributed sequences generated by a greedy minimization of the discrepancy
Ralph Kritzinger
The aim of this paper is to develop greedy algorithms which generate uniformly distributed sequences in the -dimensional unit cube . The figures of merit are three diff…
Improved dispersion bounds for modified Fibonacci lattices
Ralph Kritzinger, Jaspar Wiart
We study the dispersion of point sets in the unit square; i.e. the size of the largest axes-parallel box amidst such point sets. It is known that $\liminf_{N\to\infty} N\mathrm{dis…
Extreme and periodic discrepancy of plane point sets
Aicke Hinrichs, Ralph Kritzinger, Friedrich Pillichshammer
In this paper we study the extreme and the periodic discrepancy of plane point sets. The extreme discrepancy is based on arbitrary rectangles as test sets whereas the periodi…
Dispersion of digital -nets
Ralph Kritzinger
We study the dispersion of digital -nets; i.e. the size of the largest axes-parallel box within such point sets. Digital nets are an important class of low-discrepancy poi…
Lower bounds on the discrepancy of digital NUT sequences
Ralph Kritzinger, Friedrich Pillichshammer
We study the discrepancy of digital NUT sequences which are an important sub-class of digital -sequences in the sense of Niederreiter. The main result is a lower bound…
Extremal Distributions of Discrepancy functions
Ralph Kritzinger, Markus Passenbrunner
The irregularities of a distribution of points in the unit interval are often measured with various notions of discrepancy. The discrepancy function can be defined with respect…
Digital nets in dimension two with the optimal order of discrepancy
Ralph Kritzinger, Friedrich Pillichshammer
We study the discrepancy of two-dimensional digital nets for finite . In the year 2001 Larcher and Pillichshammer identified a class of digital nets for which the symmetri…
Finding exact formulas for the discrepancy of digital -nets via Haar functions
Ralph Kritzinger
We use the Haar function system in order to study the discrepancy of a class of digital -nets. Our approach yields exact formulas for this quantity, which measures t…
A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy
Ralph Kritzinger, Helene Laimer, Mario Neumüller
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice…
Optimal discrepancy rate of point sets in Besov spaces with negative smoothness
Ralph Kritzinger
We consider the local discrepancy of a symmetrized version of Hammersley type point sets in the unit square. As a measure for the irregularity of distribution we study the norm of…
discrepancy of symmetrized generalized Hammersley point sets in base
Ralph Kritzinger, Lisa M. Kritzinger
Two popular and often applied methods to obtain two-dimensional point sets with the optimal order of discrepancy are digit scrambling and symmetrization. In this paper we com…
An exact formula for the discrepancy of the symmetrized Hammersley point set
Ralph Kritzinger
The process of symmetrization is often used to construct point sets with low discrepancy. In the current work we apply this method to the shifted Hammersley point set. It is…
L_p- and S_{p,q}^rB-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases
Ralph Kritzinger
We study the local discrepancy of a symmetrized version of the well-known van der Corput sequence and of modified two-dimensional Hammersley point sets in arbitrary base . We gi…
A reduced fast component-by-component construction of lattice point sets with small weighted star discrepancy
Ralph Kritzinger, Helene Laimer
The weighted star discrepancy of point sets appears in the weighted Koksma-Hlawka inequality and thus is a measure for the quality of point sets with respect to their performance i…
-discrepancy of the symmetrized van der Corput sequence
Ralph Kritzinger, Friedrich Pillichshammer
It is well known that the -discrepancy for of the van der Corput sequence is of exact order of magnitude . This however is for $p \in (1,\inf…
Optimal order of -discrepancy of digit shifted Hammersley point sets in dimension 2
Aicke Hinrichs, Ralph Kritzinger, Friedrich Pillichshammer
It is well known that the two-dimensional Hammersley point set consisting of elements (also known as Roth net) does not have optimal order of -discrepancy for $p \in (…