Skip to main content
SpringerLink
Log in

Discrepancy bounds for nonoverlapping pairs of quadratic congruential pseudorandom numbers

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. Eichenauer andJ. Lehn, On the structure of quadratic congruential sequences. Manuscripta Math.58, 129–140 (1987).

    Google Scholar 

  2. J. Eichenauer-Herrmann, A remark on the discrepancy of quadratic congruential pseudorandom numbers. J. Comput. Appl. Math.43, 383–387 (1992).

    Google Scholar 

  3. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial. Internat. Statist. Rev.60, 167–176 (1992).

    Google Scholar 

  4. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers. Z. Angew. Math. Mech.73, T644-T647 (1993).

    Google Scholar 

  5. J. Eichenauer-Herrmann, On the discrepancy of quadratic congruential pseudorandom numbers with power of two modulus. J. Comput. Appl. Math.53, 371–376 (1994).

    Google Scholar 

  6. J. Eichenauer-Herrmann, Pseudorandom number generation by nonlinear methods. Internat. Statist. Rev.63, 247–255 (1995).

    Google Scholar 

  7. J. Eichenauer-Herrmann andH. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers. J. Comput. Appl. Math.34, 243–249 (1991).

    Google Scholar 

  8. 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, 649–660 (1961).

    Google Scholar 

  9. D. E.Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 2nd ed. Reading 1981.

  10. H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions. Math. Comp.52, 135–144 (1989).

    Google Scholar 

  11. H. Niederreiter, Recent trends in random number and random vector generation. Ann. Oper. Res.31, 323–345 (1991).

    Google Scholar 

  12. 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. Systems374, 145–153, Berlin New York 1992.

  13. H.Niederreiter, Finite fields, pseudorandom numbers, and quasirandom points. In: Finite Fields, Coding Theory, and Advances in Communications and Computing, G. L. Mullen and P. J. -S. Shiue, eds., 375–394, New York 1993.

  14. H.Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia 1992.

  15. H. Niederreiter, Pseudorandom numbers and quasirandom points. Z. Angew. Math. Mech.73, T648-T652 (1993).

    Google Scholar 

Download references

Author information

Author notes

  1. Jürgen Eichenauer-Herrmann

    Present address: Fachbereich Mathematik, Technische Hochschule, Schloßgartenstraße 7, D-64289, Darmstadt

Authors and Affiliations

    Authors
    1. Jürgen Eichenauer-Herrmann
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Eichenauer-Herrmann, J. Discrepancy bounds for nonoverlapping pairs of quadratic congruential pseudorandom numbers. Arch. Math 65, 362–368 (1995). https://doi.org/10.1007/BF01195549

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01195549

    Keywords

    Search

    Navigation