On a new class of pseudorandom numbers for simulation methods. (English) Zbl 0823.65010

Niederreiter, Harald

J. Comput. Appl. Math. 56, No. 1-2, 159-167 (1994).

The explicit inversive congruential method for generating pseudorandom numbers, introduced previously by J. Eichenauer-Herrmann [Math. Comput. 60, No. 201, 375-384 (1993; Zbl 0795.65002)], is discussed. The resulting pseudorandom numbers possess optimal nonlinearity property and show the best possible behavior under the lattice test. It is guaranteed that they pass the serial test and thus have desirable independence properties. The discrepancy bounds are in good accordance with the law of the iterated logarithm for discrepancies.
The method can easily generate a large number of parallel streams of pseudorandom numbers. The numbers satisfy the requirements of W. F. Eddy [J. Comput. Appl. Math. 31, No. 1, 63-71 (1990; Zbl 0703.65007)] on random number generators for parallel processors.

Reviewer: V.Burjan (Praha)

MSC:

65C10	Random number generation in numerical analysis
65Y05	Parallel numerical computation
11K45	Pseudo-random numbers; Monte Carlo methods

Keywords:

parallel computation; explicit inversive congruential method; pseudorandom numbers; lattice test; serial test; random number generators

Citations:

Zbl 0795.65002; Zbl 0703.65007

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