Pseudorandom number generation by nonlinear methods. (English) Zbl 0840.65005

Eichenauer-Herrmann, Jürgen

Int. Stat. Rev. 63, No. 2, 247-255 (1995).

A survey paper on some properties of low discrepancy sequences (LDS). The paper summarises results on LDS based on inversive congruential sequences \((y_n)\), \(y_n = \text{inv}(a^*n + b)\), \(\text{inv}(x) = x^{p + 2} \text{mod } p\), \(p\) is a prime greater than 5. The paper presents the lower and upper bounds for the discrepancy measure of the sequences \(x_n = y_n/p\). An application of the result for the generation of random numbers in parallel is mentioned.
Reviewer’s remark: The upper bound is small. It is not clear whether this fact cannot be used to test that the sequence \(x_n\) is not random.

Reviewer: J.Král (Brno)

MSC:

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

Keywords:

pseudorandom number generation; nonlinear methods; parallel computation; low discrepancy sequences; inversive congruential sequences; discrepancy measure