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Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences in $$\mathbb{F}_{2^w } $$

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

Author

Listed:
  • François Panneton

    (Université de Montréal, Département d’informatique et de recherche opérationnelle)

  • Pierre L’Ecuyer

    (Université de Montréal, Département d’informatique et de recherche opérationnelle)

Abstract

Summary We construct infinite-dimensional highly-uniform point sets for quasi-Monte Carlo integration. The successive coordinates of each point are determined by a linear recurrence in $$\mathbb{F}_{2^w } $$ , the finite field with 2w elements where w is an integer, and a mapping from this field to the interval [0, 1). One interesting property of these point sets is that almost all of their two-dimensional projections are perfectly equidistributed. We performed searches for specific parameters in terms of different measures of uniformity and different numbers of points. We give a numerical illustration showing that using randomized versions of these point sets in place of independent random points can reduce the variance drastically for certain functions.

Suggested Citation

  • François Panneton & Pierre L’Ecuyer, 2006. "Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences in $$\mathbb{F}_{2^w } $$," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 419-429, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_25
    DOI: 10.1007/3-540-31186-6_25
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