Extensions of Atanassov's Methods for Halton Sequences

Henri Faure, Christiane Lemieux, Xiaoheng Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We extend Atanassov's methods for Halton sequences in two different directions: (1) in the direction of Niederreiter (t, s) - sequences, (2) in the direction of generating matrices for Halton sequences. It is quite remarkable that Atanassov's method for classical Halton sequences applies almost "word for word" to (t, s) - sequences and gives an upper bound quite comparable to those of Sobol', Faure, and Niederreiter. But Atanassov also found a way to improve further his bound for classical Halton sequences by means of a clever scrambling producing sequences which he named modified Halton sequences. We generalize his method to nonsingular lower triangular matrices in the last part of this article.

Original languageEnglish (US)
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2010
PublisherSpringer New York LLC
Pages345-362
Number of pages18
ISBN (Print)9783642274398
DOIs
StatePublished - Jan 1 2012
Event9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland
Duration: Aug 15 2010Aug 20 2010

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume23
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
CountryPoland
CityWarsaw
Period8/15/108/20/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Extensions of Atanassov's Methods for Halton Sequences'. Together they form a unique fingerprint.

  • Cite this

    Faure, H., Lemieux, C., & Wang, X. (2012). Extensions of Atanassov's Methods for Halton Sequences. In Monte Carlo and Quasi-Monte Carlo Methods 2010 (pp. 345-362). (Springer Proceedings in Mathematics and Statistics; Vol. 23). Springer New York LLC. https://doi.org/10.1007/978-3-642-27440-4_17