ArticleOriginal scientific text

Title

An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers

Authors 1, 2

Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, F.R.G.
  2. Institut für Informationsverarbeitung, Österreichische Akademie, der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria

Bibliography

  1. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
  2. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers, Z. Angew. Math. Mech. 73 (1993), T644-T647.
  3. J. Eichenauer-Herrmann, Pseudorandom number generation by nonlinear methods, Internat. Statist. Rev., to appear.
  4. J. Eichenauer-Herrmann and H. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), 243-249.
  5. J. Kiefer, On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961), 649-660.
  6. D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms , 2nd ed., Addison-Wesley, Reading, Mass., 1981.
  7. H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345.
  8. H. Niederreiter, Nonlinear methods for pseudorandom number and vector generation, in: Simulation and Optimization, G. Pflug and U. Dieter (eds.), Lecture Notes in Econom. and Math. Systems 374, Springer, Berlin, 1992, 145-153.
  9. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992.
  10. H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652
Pages:
193-198
Main language of publication
English
Received
1994-07-18
Published
1995
Exact and natural sciences