A computational investigation of the optimal Halton sequence in QMC applications
-
Manal Bayousef
and
Michael Mascagni
Abstract
We propose the use of randomized (scrambled) quasirandom sequences for the purpose of providing practical error estimates for quasi-Monte Carlo (QMC) applications.
One popular quasirandom sequence among practitioners is the Halton sequence.
However, Halton subsequences have correlation problems in their highest dimensions, and so using this sequence for high-dimensional integrals dramatically affects the accuracy of QMC.
Consequently, QMC studies have previously proposed several scrambling methods; however, to varying degrees, scrambled versions of Halton sequences still suffer from the correlation problem as manifested in two-dimensional projections.
This paper proposes a modified Halton sequence (MHalton), created using a linear digital scrambling method, which finds the optimal multiplier for the Halton sequence in the linear scrambling space.
In order to generate better uniformity of distributed sequences, we have chosen strong MHalton multipliers up to 360 dimensions.
The proposed multipliers have been tested and proved to be stronger than several sets of multipliers used in other known scrambling methods.
To compare the quality of our proposed scrambled MHalton sequences with others, we have performed several extensive computational tests that use
Acknowledgements
We would like to thank the Florida State University Research Computing Center (rcc.fsu.edu) for access to their computing facilities. The large number of computations undertaken, some of which were very CPU-intensive, could not have been done without access to this facility. We both also wish to acknowledge the help of Dr. Hongmei Chi of Florida A & M University. This work builds upon her work in a very substantial sense. The first author also would like to show our sincere gratitude to King Abdulaziz University, and the government of the Kingdom of Saudi Arabia for the scholarship that supports the first author.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A computational investigation of the optimal Halton sequence in QMC applications
- Gillespie algorithm and diffusion approximation based on Monte Carlo simulation for innovation diffusion: A comparative study
- Wavelet-based simulation of random processes from certain classes with given accuracy and reliability
- Parallel MCMC methods for global optimization
- A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion
- Quasi-Monte Carlo method for solving Fredholm equations
- Generation of k-wise independent random variables with small randomness
- A random walk on small spheres method for solving transient anisotropic diffusion problems
Articles in the same Issue
- Frontmatter
- A computational investigation of the optimal Halton sequence in QMC applications
- Gillespie algorithm and diffusion approximation based on Monte Carlo simulation for innovation diffusion: A comparative study
- Wavelet-based simulation of random processes from certain classes with given accuracy and reliability
- Parallel MCMC methods for global optimization
- A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion
- Quasi-Monte Carlo method for solving Fredholm equations
- Generation of k-wise independent random variables with small randomness
- A random walk on small spheres method for solving transient anisotropic diffusion problems
