TY - GEN
T1 - Extensions of Atanassov's Methods for Halton Sequences
AU - Faure, Henri
AU - Lemieux, Christiane
AU - Wang, Xiaoheng
N1 - Funding Information:
We wish to thank the referee for his/her detailed comments, which were very helpful to improve the presentation of this manuscript. The second author acknowledges the support of NSERC for this work.
PY - 2012
Y1 - 2012
N2 - We extend Atanassov's methods for Halton sequences in two different directions: (1) in the direction of Niederreiter (t, s) - sequences, (2) in the direction of generating matrices for Halton sequences. It is quite remarkable that Atanassov's method for classical Halton sequences applies almost "word for word" to (t, s) - sequences and gives an upper bound quite comparable to those of Sobol', Faure, and Niederreiter. But Atanassov also found a way to improve further his bound for classical Halton sequences by means of a clever scrambling producing sequences which he named modified Halton sequences. We generalize his method to nonsingular lower triangular matrices in the last part of this article.
AB - We extend Atanassov's methods for Halton sequences in two different directions: (1) in the direction of Niederreiter (t, s) - sequences, (2) in the direction of generating matrices for Halton sequences. It is quite remarkable that Atanassov's method for classical Halton sequences applies almost "word for word" to (t, s) - sequences and gives an upper bound quite comparable to those of Sobol', Faure, and Niederreiter. But Atanassov also found a way to improve further his bound for classical Halton sequences by means of a clever scrambling producing sequences which he named modified Halton sequences. We generalize his method to nonsingular lower triangular matrices in the last part of this article.
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U2 - 10.1007/978-3-642-27440-4_17
DO - 10.1007/978-3-642-27440-4_17
M3 - Conference contribution
AN - SCOPUS:84893573819
SN - 9783642274398
T3 - Springer Proceedings in Mathematics and Statistics
SP - 345
EP - 362
BT - Monte Carlo and Quasi-Monte Carlo Methods 2010
PB - Springer New York LLC
T2 - 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
Y2 - 15 August 2010 through 20 August 2010
ER -