DISTRIBUTION PROPERTIES OF GENERALIZED VAN DER CORPUT–HALTON SEQUENCES AND THEIR SUBSEQUENCES-Reference-Cited by-同舟云学术

DISTRIBUTION PROPERTIES OF GENERALIZED VAN DER CORPUT–HALTON SEQUENCES AND THEIR SUBSEQUENCES

Published:2009-06 Issue:04 Volume:05 Page:719-746
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

HOFER ROSWITHA¹,KRITZER PETER²,LARCHER GERHARD¹,PILLICHSHAMMER FRIEDRICH¹

Affiliation:

1. Institut für Finanzmathematik, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria

2. Fachbereich Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020 Salzburg, Austria

Abstract

We study the distribution properties of sequences which are a generalization of the well-known van der Corput–Halton sequences on one hand, and digital (T,s)-sequences on the other. In this paper, we give precise results concerning the distribution properties of such sequences in the s-dimensional unit cube. Moreover, we consider subsequences of the above-mentioned sequences and study their distribution properties. Additionally, we give discrepancy estimates for some special cases, including subsequences of van der Corput and van der Corput–Halton sequences.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042109002328

Reference21 articles.

1. Foundation of Computing Series;Bach E.,1996

2. A summation formula related to the binary digits

3. Lecture Notes in Mathematics;Drmota M.,1997

Cited by 28 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Copulas;Uniform distribution theory;2023-07-01

2. On Hybrid Point Sets Stemming from Halton-Type Hammersley Point Sets and Polynomial Lattice Point Sets;Springer Proceedings in Mathematics & Statistics;2020

3. Multistart method with deterministic restart mechanism;Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes;2020

4. Tractability of $\mathbb{L}_2$-approximation in hybrid function spaces;Functiones et Approximatio Commentarii Mathematici;2018-03-01

5. Kronecker–Halton sequences in Fp((X−1));Finite Fields and Their Applications;2018-03