Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
ACM Transactions on Mathematical Software (TOMS)
Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
SIAM Journal on Numerical Analysis
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Quasi-random integration in high dimensions
Mathematics and Computers in Simulation
Parallel quasirandom number generations for heterogeneous computing environments
International Journal of Parallel, Emergent and Distributed Systems
On efficient Monte Carlo-based statistical static timing analysis of digital circuits
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Generating inverse Gaussian random variates by approximation
Computational Statistics & Data Analysis
An efficient implementation of a least squares Monte Carlo method for valuing American-style options
International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
Acceleration of market value-at-risk estimation
Proceedings of the 2nd Workshop on High Performance Computational Finance
Visual exploration of algorithm parameter space
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
A novel particle swarm niching technique based on extensive vector operations
Natural Computing: an international journal
Effect of particle initialization on the performance of particle swarm niching algorithms
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On the scrambled soboĺ sequence
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Tuning the generation of sobol sequence with owen scrambling
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Accelerating Value-at-Risk estimation on highly parallel architectures
Concurrency and Computation: Practice & Experience
Numerical quadrature for high-dimensional singular integrals over parallelotopes
Computers & Mathematics with Applications
Objective image quality assessment of texture compression
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
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An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and "direction numbers" so as to allow the generation of Sobol' sequences to approximate integrals in up to 1111 dimensions. The direction numbers given generate Sobol' sequences that satisfy Sobol's so-called Property A.