Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Van der Corput sequences, Kakutani transforms and one-dimensional numerical integration
Journal of Computational and Applied Mathematics
Polynomial arithmetic analogue of Halton sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Fast generation of low-discrepancy sequences
Journal of Computational and Applied Mathematics
Algorithmic number theory
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Quasirandom points and global function fields
FFA '95 Proceedings of the third international conference on Finite fields and applications
Faster evaluation of multidimensional integrals
Computers in Physics
On the L2-discrepancy for anchored boxes
Journal of Complexity
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Generating and Testing the Modified Halton Sequences
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
Improved upper bounds on the star discrepancy of (t, m, s)-nets and (t, s)-sequences
Journal of Complexity
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy
Journal of Computational and Applied Mathematics
On the optimal Halton sequence
Mathematics and Computers in Simulation
Mathematical and Computer Modelling: An International Journal
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Hi-index | 0.00 |
Halton sequences have always been quite popular with practitioners, in part because of their intuitive definition and ease of implementation. However, in their original form, these sequences have also been known for their inadequacy to integrate functions in moderate to large dimensions, in which case (t,s)-sequences such as the Sobol' sequence are usually preferred. To overcome this problem, one possible approach is to include permutations in the definition of Halton sequences—thereby obtaining generalized Halton sequences—an idea that goes back to almost thirty years ago, and that has been studied by many researchers in the last few years. In parallel to these efforts, an important improvement in the upper bounds for the discrepancy of Halton sequences has been made by Atanassov in 2004. Together, these two lines of research have revived the interest in Halton sequences. In this article, we review different generalized Halton sequences that have been proposed recently, and compare them by means of numerical experiments. We also propose a new generalized Halton sequence which, we believe, offers a practical advantage over the surveyed constructions, and that should be of interest to practitioners.