Constructing adapted lattice rules using problem-dependent criteria

Authors:
Pierre L'Ecuyer;David Munger
Affiliations:
Université de Montreal, Montréal (Québec), Canada;Université de Montreal, Montréal (Québec), Canada
Venue:
Proceedings of the Winter Simulation Conference
Year:
2012

Citing 15
Cited 0

Random number generation and quasi-Monte Carlo methods

Random number generation and quasi-Monte Carlo methods
Latin supercube sampling for very high-dimensional simulations

ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A generalized discrepancy and quadrature error bound

Mathematics of Computation
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?

Journal of Complexity
Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature

SIAM Journal on Scientific Computing
Component-by-component construction of good lattice rules with a composite number of points

Journal of Complexity
The existence of good extensible rank-1 lattices

Journal of Complexity
Variance Reduction via Lattice Rules

Management Science
Liberating the weights

Journal of Complexity
Efficient Weighted Lattice Rules with Applications to Finance

SIAM Journal on Scientific Computing
Constructing Robust Good Lattice Rules for Computational Finance

SIAM Journal on Scientific Computing
Constructing Embedded Lattice Rules for Multivariate Integration

SIAM Journal on Scientific Computing
Multilevel Monte Carlo Path Simulation

Operations Research
Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Variance bounds and existence results for randomly shifted lattice rules

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We describe a new software tool named Lattice Builder, designed to construct lattice point sets for quasi-Monte Carlo integration via randomly-shifted lattice rules. This tool permits one to search for good lattice parameters in terms of various uniformity criteria, for an arbitrary number of points and arbitrary dimension. It also constructs lattices that are extensible in the number of points and in the dimension. A numerical illustration is given.