TY - GEN
T1 - Implementation of a component-by-component algorithm to generate small low-discrepancy samples
AU - Doerr, Benjamin
AU - Gnewuch, Michael
AU - Wahlström, Magnus
PY - 2009/1/1
Y1 - 2009/1/1
N2 - In [B. Doerr, M. Gnewuch, P. Kritzer, F. Pillichshammer. Monte Carlo Methods Appl., 14:129-149, 2008], a component-by-component (CBC) approach to generate small low-discrepancy samples was proposed and analyzed. The method is based on randomized rounding satisfying hard constraints and its derandomization. In this paper we discuss how to implement the algorithm and present first numerical experiments. We observe that the generated points in many cases have a significantly better star discrepancy than what is guaranteed by the theoretical upper bound. Moreover, we exhibit that the actual discrepancy is mainly caused by the underlying grid structure, whereas the rounding errors have a negligible contribution. Hence to improve the algorithm, we propose and analyze a randomized point placement. We also study a hybrid approach which combines classical low-discrepancy sequences and the CBC algorithm.
AB - In [B. Doerr, M. Gnewuch, P. Kritzer, F. Pillichshammer. Monte Carlo Methods Appl., 14:129-149, 2008], a component-by-component (CBC) approach to generate small low-discrepancy samples was proposed and analyzed. The method is based on randomized rounding satisfying hard constraints and its derandomization. In this paper we discuss how to implement the algorithm and present first numerical experiments. We observe that the generated points in many cases have a significantly better star discrepancy than what is guaranteed by the theoretical upper bound. Moreover, we exhibit that the actual discrepancy is mainly caused by the underlying grid structure, whereas the rounding errors have a negligible contribution. Hence to improve the algorithm, we propose and analyze a randomized point placement. We also study a hybrid approach which combines classical low-discrepancy sequences and the CBC algorithm.
U2 - 10.1007/978-3-642-04107-5_20
DO - 10.1007/978-3-642-04107-5_20
M3 - Conference contribution
AN - SCOPUS:84904094998
SN - 9783642041068
T3 - Monte Carlo and Quasi-Monte Carlo Methods 2008
SP - 323
EP - 338
BT - Monte Carlo and Quasi-Monte Carlo Methods 2008
PB - Springer Verlag
T2 - 8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008
Y2 - 6 July 2008 through 11 July 2008
ER -