89
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

New Modified Scrambled Faure Sequences

&
Pages 666-682 | Received 20 May 2012, Accepted 22 Mar 2013, Published online: 10 Sep 2014

References

  • Bratley, P., Fox, B., Niederreiter, H. (1992). Implementation and tests of low-discrepancy sequences. ACM Trans. on Modelling and Computer Simulation 2(3):195–213.
  • Chi, H. (2004). Scrambled Quasirandom Sequences and their Applications . Ph.D. Dissertation, Tallahassee, FL: Florida State University.
  • Chi, H., Mascagni, M., Warnock, T. (2005). On the optimal Halton sequences. Mathematics and Computers in Simulation 70(1):9–21.
  • Eichenauer, J., Grothe, H., Lehn, J. (1988). Marsaglia’s lattice test and nonlinear congruential pseudo random number generators. Metrika 35:241–250.
  • Eichenauer, J., Lehn, J. (1986). A non-linear congruential pseudo random number generator. Statistische Hefte 27:315–326.
  • Eichenauer, J., Niederreiter, H. (1988). On Marsaglia’s lattice test for pseudorandom numbers. Manuscripta Mathematica 62:245–248.
  • Vajargah, B., Chechaglou, A. (2013). Optimal Halton sequence via inversive Scrambling. Communications in Statistics – Simulation and Computation 42:476–484.
  • Faure, H. (1982). Discrepancy of sequences associated with a number system (in dimension s). Acta Arithmetica 41(4):337–351.
  • Faure, H. (2001). Variations on (0,s)-sequences. Journal of Complexity 17(4):741–753.
  • Faure, H., Lemieux, C. (2009). Generalized Halton sequences in 2008: A comparative study. ACM Transactions on Modeling and Computer Simulation 19(4):1–15, Article 15.
  • Fox, B.L. (1986). Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators. ACM Transactions on Mathematical Software 12(4):362–376.
  • Joe, S., Kuo, F.Y. (2008). Construncing Sobol sequences with better two-dimensional projections. SIAM Journal on Scientific Computing 30(5):2635–2654.
  • Lehmer, D.H. (1949). Mathematical methods in large-scale computing units. In: Proc. 2nd Sympos. on Large-Scale Digital Calculating Machinery, MA: Cambridge, pp. 141–146.
  • Matoušek’s, J. (1998). On the L2-discrepancy for anchored boxes. Journal of Complexity 14:527–556.
  • Niederreiter, H. (1978). Quasi-Monte Carlo methods and pseudo-random numbers. Bulletin of the American Mathematical Society 84:9571041.
  • Niederreiter, H. (1987). Point sets and sequences with small discrepancy. Monatshefte fr Mathematik 104:273–337.
  • Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. Philadephia, PA: SIAM.
  • Niederreiter, H., Xing, C. (1996). Quasirandom points and global function fields. In: Finite fields and applications (Glasgow, 1995). London Math. Soc. Lecture Note Ser., vol. 233. . (S. D. Cohen and H. Niederreiter, eds.) Cambridge: Cambridge Univ. Press., pp. 269–296.
  • Owen, A.B. (2000). Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo. In: Niederreiter, H., Spanier, J., eds., Monte Carlo and Quasi-Monte Carlo Methods 1998. Berlin Heidelberg. Springer-Verlag, pp. 86–97.
  • Owen, A.B. (2003). Variance with alternative scramblings of digital nets. ACM Transactions on Modeling and Computer Simulation 13:363–378.
  • Spanier, J., Maize, E.H. (1994). Quasi-random methods for estimating integrals using relatively small samples. SIAM Review 36(1):18–44.
  • Tezuka, S. (1994). A generalization of Faure sequences and its efficient implementation. Technical Report RT0105, IBM. Tokyo Research Laboratory.
  • Tezuka, S. (1995). Uniform Random Numbers, Theory and Practice. New York: Kluwer Academic Publishers.
  • Tezuka, S., Faure, H. (2003). I-binomial scrambling of digital nets and sequences. Journal of Complexity 19(6):744–757.
  • Vandewoestyne, B., Chi, H., Cools, R. (2010). Computational investigations of scrambled faure sequences. Mathematics and Computers in Simulation 81:522–535.
  • Wang, X., Fang, K.T. (2003). The effective dimension and quasi-Monte Carlo. Journal of Complexity 19(2):101–124.
  • Warnock, T. (1995). Computational investigations of low discrepancy point sets II. In: Niederreiter, H., ed. Monte Carlo and quasi-Monte Carlo Methods in Scientific Computing, New York: Springer, pp. 354–361.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.