Randomized Halton sequences

Xiaoqun Wang*, F. J. Hickernell

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

151 Citations (Scopus)

Abstract

The Halton sequence is a well-known multi-dimensional low-discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence. This randomization makes use of the description of Halton sequence using the von Neumann-Kakutani transformation. We randomize the starting point of the sequence. This method combines the potential accuracy advantage of Halton sequence in multi-dimensional integration with the practical error estimation advantage of Monte Carlo methods. Theoretically, using multiple randomized Halton sequences as a variance reduction technique we can obtain an efficiency improvement over standard Monte Carlo. Numerical results show that randomized Halton sequences have better performance not only than Monte Carlo, but also than randomly shifted Halton sequences. They have similar performance with the randomly digit-scrambled Halton sequences but require much less generating time.

Original languageEnglish
Pages (from-to)887-899
Number of pages13
JournalMathematical and Computer Modelling
Volume32
Issue number7-8
DOIs
Publication statusPublished - Oct 2000
Externally publishedYes

Scopus Subject Areas

  • Modelling and Simulation
  • Computer Science Applications

User-Defined Keywords

  • Low-discrepancy sequences
  • Monte Carlo methods
  • Numerical integration
  • Quasi-Monte Carlo methods
  • Variance reduction

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