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Journal of Computational and Applied Mathematics
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
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Fast generation of low-discrepancy sequences
Journal of Computational and Applied Mathematics
The mean square discrepancy of randomized nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
A generalized discrepancy and quadrature error bound
Mathematics of Computation
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
On the L2-discrepancy for anchored boxes
Journal of Complexity
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
ACM Transactions on Mathematical Software (TOMS)
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places
Finite Fields and Their Applications
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Genetic algorithms using low-discrepancy sequences
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Efficient simulated maximum likelihood with an application to online retailing
Statistics and Computing
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
PSO with randomized low-discrepancy sequences
Proceedings of the 9th annual conference on Genetic and evolutionary computation
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Robotics and Autonomous Systems
Applied Numerical Mathematics
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TestCom '08 / FATES '08 Proceedings of the 20th IFIP TC 6/WG 6.1 international conference on Testing of Software and Communicating Systems: 8th International Workshop
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Formal Methods in System Design
Generalized Halton sequences in 2008: A comparative study
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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
Parameterization based on randomized quasi-Monte Carlo methods
Parallel Computing
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the use of randomized low-discrepancy sequences in sampling-based motion planning
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
Computation of the endogenous mortgage rates with randomized quasi-Monte Carlo simulations
Mathematical and Computer Modelling: An International Journal
Random sampling from low-discrepancy sequences: applications to option pricing
Mathematical and Computer Modelling: An International Journal
Temporally coherent adaptive sampling for imperfect shadow maps
EGSR '13 Proceedings of the Eurographics Symposium on Rendering
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The Halton sequence is a well-known multi-dimensional low-discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence. This randomization makes use of the description of Halton sequence using the von Neumann-Kakutani transformation. We randomize the starting point of the sequence. This method combines the potential accuracy advantage of Halton sequence in multi-dimensional integration with the practical error estimation advantage of Monte Carlo methods. Theoretically, using multiple randomized Halton sequences as a variance reduction technique we can obtain an efficiency improvement over standard Monte Carlo. Numerical results show that randomized Halton sequences have better performance not only than Monte Carlo, but also than randomly shifted Halton sequences. They have similar performance with the randomly digit-scrambled Halton sequences but require much less generating time.