Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Multidimensional quadrature algorithms
Computers in Physics
Computing the discrepancy with applications to supersampling patterns
ACM Transactions on Graphics (TOG)
Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
SIAM Journal on Numerical Analysis
On the L2-discrepancy for anchored boxes
Journal of Complexity
Fast convergence of quasi-Monte Carlo for a class of isotropic integrals
Mathematics of Computation
Error bounds for Quasi-Monte Carlo integration with uniform point sets
Journal of Computational and Applied Mathematics
Generating low-discrepancy sequences from the normal distribution: Box-Muller or inverse transform?
Mathematical and Computer Modelling: An International Journal
A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting
SIAM Journal on Numerical Analysis
| Hi-index | 7.29 |
Monte Carlo and quasi-Monte Carlo methods are popular numerical tools used in many applications. The quality of the pseudorandom sequence used in a Monte Carlo simulation is essential to the accuracy of its estimates. Likewise, the quality of the low-discrepancy sequence determines the accuracy of a quasi-Monte Carlo simulation. There is a vast literature on statistical tests that help us assess the quality of a pseudorandom sequence. However, for low-discrepancy sequences, assessing quality by estimating discrepancy is a very challenging problem, leaving us with no practical options in very high dimensions. In this paper, we will discuss how a certain interpretation of the well-known collision test for pseudorandom sequences can be used to obtain useful information about the quality of low-discrepancy sequences. Numerical examples will be used to illustrate the applications of the collision test.