Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasi-Monte Carlo set of tools. A theoretical framework for a class of lattice rules defined in a space of polynomials with coefficients in a finite field is developed in this paper....

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 24; no. 5; pp. 1768 - 1789
Main Authors: Lemieux, Christiane, L'Ecuyer, Pierre
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2003
Subjects:
Algebra
Combinatorics. Ordered structures
Estimates
Exact sciences and technology
Mathematical analysis
Mathematics
Measure and integration
Monte Carlo simulation
Number theory
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Order, lattices, ordered algebraic structures
Random variables
Scholarships & fellowships
Sciences and techniques of general use
Polynomial
Finite field
Monte Carlo method
Integration
Numerical analysis
Integral
Stochastic method
Random number generation
Implementation
Variance
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasi-Monte Carlo set of tools. A theoretical framework for a class of lattice rules defined in a space of polynomials with coefficients in a finite field is developed in this paper. A randomized version is studied, implementations and criteria for selecting the parameters are discussed, and examples of its use as a variance reduction tool in stochastic simulation are provided. Certain types of digital net constructions, as well as point sets constructed by taking all vectors of successive output values produced by a Tausworthe random number generator, are special cases of this method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827501393782