A non-linear congruential pseudo random number generator

Abstract.Pseudorandom vectors are of importance for parallelized simulation methods. In this paper we carry out an in-depth analysis of the multiplerecursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author. We study, in particular, the periodicity properties, the lattice structure, and the behavior under the serial test for sequences of pseudorandom vectors generated by this method.

Section: Introductionmentioning

confidence: 99%

Pseudorandom vector generation by the multiple-recursive matrix method

Niederreiter¹

1995

“…A particularly attractive method of this type is based on achieving nonlinearity by employing the operation of multiplicative inversion with respect to a prime modulus. This inversive congruential method was introduced by Eichenauer and Lehn [2].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Lower bounds for the discrepancy of inversive congruential pseudorandom numbers

Niederreiter¹

1990

Abstract.The inversive congruential method is a uniform pseudorandom number generator which was introduced recently. For a prime modulus p the discrepancy D of k-tuples of successive pseudorandom numbers generated by this method determines the statistical independence properties of these pseudorandom numbers. It was shown earlier by the author thatHere it is proved that this bound is essentially best possible. In fact, for a positive proportion of the admissible parameters in the inversive congruential method the discrepancy D ' is at least of the order of magnitude p~ for all k > 2 .

“…The generation of uniform pseudorandom numbers in the interval [0, 1) and of uniform pseudorandom vectors in the interval [0, 1) k is a basic and crucial task in any stochastic simulation. A review of several methods is given in Niederreiter's monograph [12].…”

Section: Introductionmentioning

confidence: 99%

“…Since the simple nature of the classical linear congruential method for the generation of pseudorandom numbers and of the matrix method for the generation of pseudorandom vectors implies undesirable regularities (cf. [1]), several nonlinear methods for the generation of pseudorandom numbers and of pseudorandom vectors have been introduced [1,2,4,5,10,11,13]. A particularly attractive nonlinear approach is the inversive congruential method for the generation of pseudorandom numbers (cf.…”

Section: Introductionmentioning

confidence: 99%

“…A particularly attractive nonlinear approach is the inversive congruential method for the generation of pseudorandom numbers (cf. [1,2,5]) and the inversive method for the generation of pseudorandom vectors, which was introduced in [9] and is analyzed in detail in [14]. In [3] a compound version of the inversive congruential method for the generation of pseudorandom numbers was introduced in order to achieve a very long period length and an algorithm which allows a simple parallelized implementation.…”

Section: Introductionmentioning

confidence: 99%

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Pseudorandom vector generation by the compound inversive method

Emmerich

1996

Abstract. Pseudorandom vectors are of importance for parallelized simulation methods. In this paper a detailed analysis of the compound inversive method for the generation of k-dimensional uniform pseudorandom vectors, a vector analog of the compound inversive method for pseudorandom number generation, is carried out. In particular, periodicity properties and statistical independence properties of the generated sequences are studied based on the discrete discrepancy of s-tuples of successive terms in the sequence. The results show that the generated sequences have attractive statistical independence properties for pseudorandom vectors of dimensions k ≤ 4.