## Fast Generation of Low-Discrepancy Sequences

• The paper presents a fast implementation of a constructive method to generate a special class of low-discrepancy sequences which are based on Van Neumann-Kakutani tranformations. Such sequences can be used in various simulation codes where it is necessary to generate a certain number of uniformly distributed random numbers on the unit interval.; From a theoretical point of view the uniformity of a sequence is measured in terms of the discrepancy which is a special distance between a finite set of points and the uniform distribution on the unit interval.; Numerical results are given on the cost efficiency of different generators on different hardware architectures as well as on the corresponding uniformity of the sequences. As an example for the efficient use of low-discrepancy sequences in a complex simulation code results are presented for the simulation of a hypersonic rarefied gas flow.

Author: Jens Struckmeier urn:nbn:de:hbz:386-kluedo-7006 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (93) Preprint English 1993 1993 Technische Universität Kaiserslautern 2000/04/03 Low-discrepancy sequences ; Monte Carlo method; Van Neumann-Kakutani transformation J. Comp. & Appl. Math., Vol. 61, 29-41 (1995) Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 11-XX NUMBER THEORY / 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithms / 11K45 Pseudo-random numbers; Monte Carlo methods 65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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