Randomized Halton sequences

The Halton sequence is a well-known multi-dimensional low-discrepancy seque nce. In this paper, we propose a new method for randomizing the Halton sequ ence. This randomization makes use of the description of Halton sequence us ing the von Neumann-Kakutani transformation. We randomize the starting poin t 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 sho w that randomized Halton sequences have better performance not only than Mo nte Carlo, but also than randomly shifted Halton sequences. They have simil ar performance with the randomly digit-scrambled Halton sequences but requi re much less generating time. (C) 2000 Elsevier Science Ltd. All rights res erved.