Quasi-Monte Carlo Node Sets from Linear Congruential Generators

Entacher, Karl; Hellekalek, Peter; L’Ecuyer, Pierre

doi:10.1007/978-3-642-59657-5_12

Cited by 20 publications

(13 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…QMC techniques improve the probabilistic error bounds of MC techniques especially in higher dimensions. Nevertheless, these techniques are related [7] since a full period random number sequence may be seen as a low-discrepancy point set (e.g. a rank-1 lattice rule in the case of a linear congruential generator) as well.…”

Section: Introductionmentioning

confidence: 99%

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Hofbauer

Uhl

Zinterhof

2006

Parallel Process. Lett.

View full text Add to dashboard Cite

The splitting of Quasi-Monte Carlo (QMC) point sequences into interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower the traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the proposals made in literature so far. In numerical integration experiments we investigate the quality of single leaped QMC point sequence substreams, comparing the respective properties of Sobol', Halton, Faure, Niederreiter-Xing, and Zinterhof sequences in detail. Numerical integration results obtained on a distributed system show that leaping sensitivity varies tremendously among the different sequences and we provide examples of deteriorated results caused by leaping effects, especially in heterogeneous settings which would be expected in GRID environments.

show abstract

Section: Introductionmentioning

confidence: 99%

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Hofbauer

Uhl

Zinterhof

2006

Parallel Process. Lett.

View full text Add to dashboard Cite

show abstract

“…To obtain this excellent error behavior it is necessary to provide lattices that are optimally chosen with respect to certain measures of uniform distribution [18,30,38]. An important candidate for such a measure is the spectral test [12,19,24], which allows a very efficient and effective quality analysis for lattices up to high dimensions.…”

Section: Introductionmentioning

confidence: 99%

Efficient lattice assessment for LCG and GLP parameter searches

2001

Self Cite

View full text Add to dashboard Cite

Abstract. In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi-Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically demonstrate the speed-up and the quality loss obtained by the LLL reduction, and we present important applications for parameter selections.

show abstract

“…If P n has n points, then each coordinate of each vector of L t is a multiple of 1/n. A simple and convenient way to construct P n is to take the set of all tdimensional vectors of successive output values from a linear congruential generator (LCG) [10,18,24]; that is, take P n as the set of all vectors (u 0 , . .…”

mentioning

confidence: 99%

“…with weights w(h) that decrease with h in a way that corresponds to how we think the squared Fourier coefficients |f (h)| 2 decrease with h , and where · is an arbitrary norm (see, e.g., [10,14,16,26]). For a given choice of weights w(h), either definition of D(P n ) in (2.4) can be used as a selection criterion (to be minimized) over a given set of n-point lattice rules.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

Lemieux

L’Ecuyer²

2003

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. 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.

show abstract

Quasi-Monte Carlo Node Sets from Linear Congruential Generators

Cited by 20 publications

References 17 publications

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Efficient lattice assessment for LCG and GLP parameter searches

Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

Contact Info

Product

Resources

About