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

François Panneton () and Pierre L’Ecuyer ()
Additional contact information
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

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 419-429 from Springer

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.

Keywords: Monte Carlo; Linear Recurrence; Lattice Rule; Dimensional Projection; Unit Hypercube (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_25

Ordering information: This item can be ordered from
http://www.springer.com/9783540311867

DOI: 10.1007/3-540-31186-6_25

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().