research-article

Generalized Halton sequences in 2008: A comparative study

Authors:

Christiane LemieuxAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 19, Issue 4

Article No.: 15, Pages 1 - 31

https://doi.org/10.1145/1596519.1596520

Published: 04 November 2009 Publication History

Abstract

Halton sequences have always been quite popular with practitioners, in part because of their intuitive definition and ease of implementation. However, in their original form, these sequences have also been known for their inadequacy to integrate functions in moderate to large dimensions, in which case (t,s)-sequences such as the Sobol' sequence are usually preferred. To overcome this problem, one possible approach is to include permutations in the definition of Halton sequences—thereby obtaining generalized Halton sequences—an idea that goes back to almost thirty years ago, and that has been studied by many researchers in the last few years. In parallel to these efforts, an important improvement in the upper bounds for the discrepancy of Halton sequences has been made by Atanassov in 2004. Together, these two lines of research have revived the interest in Halton sequences. In this article, we review different generalized Halton sequences that have been proposed recently, and compare them by means of numerical experiments. We also propose a new generalized Halton sequence which, we believe, offers a practical advantage over the surveyed constructions, and that should be of interest to practitioners.

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Faure Appendix (a15-faure-apndx.pdf)

Online appendix to generalized Halton sequences in 2008: A comparative study. The appendix supports the information on article 15.

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Index Terms

Generalized Halton sequences in 2008: A comparative study
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
    2. Quadrature
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 19, Issue 4

October 2009

151 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/1596519

Issue’s Table of Contents

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 04 November 2009

Accepted: 01 November 2008

Revised: 01 May 2008

Received: 01 June 2007

Published in TOMACS Volume 19, Issue 4

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Kang BHughes JHaran M(2024)Fast Bayesian Inference for Spatial Mean-Parameterized Conway–Maxwell–Poisson ModelsJournal of Computational and Graphical Statistics10.1080/10618600.2024.2394460(1-18)Online publication date: 21-Aug-2024
https://doi.org/10.1080/10618600.2024.2394460
Rusch TKirk NBronstein MLemieux CRus D(2024)Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networksProceedings of the National Academy of Sciences10.1073/pnas.2409913121121:40Online publication date: 26-Sep-2024
https://doi.org/10.1073/pnas.2409913121
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