Quasi-Monte Carlo integration is a method of numerical integration that operates in the same way as Monte
Carlo integration, but instead uses sequences of quasirandom
numbers to compute the integral. Quasirandom numbers are generated algorithmically
by computer, and are similar to pseudorandom numbers
while having the additional important property of being deterministically chosen
based on equidistributed sequences (Ueberhuber 1997, p. 125) in order to minimize
errors.
Monte Carlo methods are connected with computer simulation, and there is a distinction between simulation (where the system investigated
and the mathematical model are both stochastic in nature, as in the simulation of
a supermarket), and Monte Carlo simulation (where the modeled system is deterministic
and the model used is stochastic) as in the case of Monte Carlo integration (Neelamkaville
1987, p. 3).
A quasi-Monte Carlo method known as the Halton-Hammersley-Wozniakowski algorithm is implemented in the Wolfram Language
as NIntegrate[f,
..., Method ->QuasiMonteCarlo].
Hammersley, J. M. "Monte Carlo Methods for Solving Multivariable Problems." Ann. New York Acad. Sci.86, 844-874,
1960.Hammersley, J. M. and Handscomb, D. C. Monte
Carlo Methods. New York: Wiley, p. 25, 1964.Neelamkavil,
F. Computer
Simulation and Modelling. New York: Wiley, pp. 3-4, 1987.Ueberhuber,
C. W. Numerical
Computation 2: Methods, Software, and Analysis. Berlin:Springer-Verlag, pp. 124-125,
1997.Weinzierl, S. "Introduction to Monte Carlo Methods."
23 Jun 2000. http://arxiv.org/abs/hep-ph/0006269.Wolfram,
S. A
New Kind of Science. Champaign, IL: Wolfram Media, p. 1085,
2002.Wozniakowski, H. "Average Case Complexity of Multivariate
Integration." Bull. Amer. Math. Soc.24, 185-194, 1991.
