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Optimal characteristic polynomials for digital multistep pseudorandom numbers

Optimale charakteristische Polynome für Pseudozufallszahlen nach der digitalen Mehrschrittmethode

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Abstract

The digital multistep method generates uniform pseudorandom numbers by transforming sequences of integers obtained by multistep recursions. The statistical independence properties of these pseudorandom numbers depend on the characteristic polynomial of the recursion. We describe a method of calculating characteristic polynomials that are optimal with respect to statistical independence of pairs of successive pseudorandom numbers. Tables of such optimal characteristic polynomials for degrees ≤64 are included.

Zusammenfassung

Die digitale Mehrschrittmethode erzeugt gleichverteilte Pseudozufallszahlen durch Transformation von Folgen ganzer Zahlen, die aus Rekursionen höherer Ordnung gewonnen werden. Die statistischen Unabhängigkeitseigenschaften dieser Pseudozufallszahlen hängen vom charakteristischen Polynom der Rekursion ab. Es wird eine Methode zur Berechnung von charakteristischen Polynomen beschrieben, welche bezüglich der statistischen Unabhängigkeit von Paaren aufeinanderfolgender Pseudozufallszahlen optimal sind. Die Arbeit enthält auch Tabellen solcher optimaler charakteristischer Polynome für Grade ≤64.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, U.S.A.

    G. L. Mullen

  2. Mathematical Institute, Austrian Academy of Sciences, Dr. Ignaz Seipel-Platz 2, A-1010, Vienna, Austria

    H. Niederreiter

Authors
  1. G. L. Mullen
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  2. H. Niederreiter
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Mullen, G.L., Niederreiter, H. Optimal characteristic polynomials for digital multistep pseudorandom numbers. Computing 39, 155–163 (1987). https://doi.org/10.1007/BF02310104

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  • DOI: https://doi.org/10.1007/BF02310104

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