On a new class of inversive pseudorandom numbers for parallelized simulation methods

Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the digital explicit inversive method recently introduced by the authors. We establish some new results on the statistical properties of parallel streams of pseudorandom numbers generated by this method. In particular, we extend the results of the first author on the statistical properties of pseudorandom numbers generated by the explicit inversive congruential method introduced by Eichenauer-Herrmann. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties.

[1]  Harald Niederreiter,et al.  Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators , 2000 .

[2]  Igor E. Shparlinski,et al.  On the Distribution and Lattice Structure of Nonlinear Congruential Pseudorandom Numbers , 1999 .

[3]  Igor E. Shparlinski,et al.  On the Distribution of Pseudorandom Numbers and Vectors Generated by Inversive Methods , 2000, Applicable Algebra in Engineering, Communication and Computing.

[4]  J. Eichenauer-Herrmann.  Statistical independence of a new class of inversive congruential pseudorandom numbers , 1993 .

[5]  Harald Niederreiter,et al.  Introduction to finite fields and their applications: List of Symbols , 1986 .

[6]  Oscar Moreno,et al.  Exponential sums and Goppa codes. I , 1991 .

[7]  Harald Niederreiter,et al.  On the Lattice Structure of Pseudorandom Numbers Generated over Arbitrary Finite Fields , 2001, Applicable Algebra in Engineering, Communication and Computing.

[8]  Peter Hellekalek,et al.  General discrepancy estimates: the Walsh function system , 1994 .

[9]  Harald Niederreiter,et al.  On a new class of pseudorandom numbers for simulation methods , 1994 .

[10]  G. Marsaglia.  The Structure of Linear Congruential Sequences , 1972 .

[11]  Igor E. Shparlinski,et al.  On the distribution of inversive congruential pseudorandom numbers in parts of the period , 2001, Math. Comput..

[12]  H. Niederreiter.  Improved Bounds in the Multiple-Recursive Matrix Method for Pseudorandom Number and Vector Generation , 1996 .

[13]  Oscar Moreno,et al.  Exponential sums and Goppa codes: II , 1989, IEEE Trans. Inf. Theory.

[14]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.