Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature

Authors:
Fred J. Hickernell;Hee Sun Hong;Pierre LÉcuyer;Christiane Lemieux
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2000

Citing 0
Cited 9

The distribution of the discrepancy of scrambled digital (t, m, s)-nets

Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Algorithm 823: Implementing scrambled digital sequences

ACM Transactions on Mathematical Software (TOMS)
The existence of good extensible rank-1 lattices

Journal of Complexity
My dream quadrature rule

Journal of Complexity
Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation

Proceedings of the 35th conference on Winter simulation: driving innovation
Searching for extensible Korobov rules

Journal of Complexity
Why quasi-Monte Carlo is better than monte carlo or latin hypercube sampling for statistical circuit analysis

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Weighted compound integration rules with higher order convergence for all N

Numerical Algorithms
Constructing adapted lattice rules using problem-dependent criteria

Proceedings of the Winter Simulation Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

Integration lattices are one of the main types of low discrepancy sets used in quasi-Monte Carlo methods. However, they have the disadvantage of being of fixed size. This article describes the construction of an infinite sequence of points, the first bm of which forms a lattice for any nonnegative integer m. Thus, if the quadrature error using an initial lattice is too large, the lattice can be extended without discarding the original points. Generating vectors for extensible lattices are found by minimizing a loss function based on some measure of discrepancy or nonuniformity of the lattice. The spectral test used for finding pseudorandom number generators is one important example of such a discrepancy. The performance of the extensible lattices proposed here is compared to that of other methods for some practical quadrature problems.