Recent trends in random number and random vector generation
Annals of Operations Research
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A course in computational algebraic number theory
A course in computational algebraic number theory
The mean square discrepancy of randomized nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A generalized discrepancy and quadrature error bound
Mathematics of Computation
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)
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
I-binomial scrambling of digital nets and sequences
Journal of Complexity
Scrambled quasirandom sequences and their applications
Scrambled quasirandom sequences and their applications
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
| Hi-index | 0.00 |
The Faure sequence is one of the well-known quasi-random sequences used in quasi-Monte Carlo applications. In its original and most basic form, the Faure sequence suffers from correlations between different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this problem is to use a randomly scrambled version of the Faure sequence. We analyze various scrambling methods and propose a new nonlinear scrambling method, which has similarities with inversive congruential methods for pseudo-random number generation. We demonstrate the usefulness of our scrambling by means of two-dimensional projections and integration problems.