On the average distribution of inversive pseudorandom numbers
Nonlinear methods are attractive alternatives to linear methods for pseudorandom number generation. In particular the inversive methods have many desirable features [see e.g. the author's survey, Recent advances in the theory of nonlinear pseudorandom number generators. Proc. Conf. Monte Carlo and quasi-Monte Carlo methods 2000, Hong Kong, Berlin: Springer, 86--102 (2002; Zbl 1076.65008)]. Here the behaviour of inversive pseudorandom numbers on average over all initial values is investigated. The results are much stronger than for the worst case [see \textit{J. Gutierrez} and the authors, Monatsh. Math. 129, 31--36 (2000; Zbl 1011.11053) and the authors, Appl. Algebra Eng. Commun. Comput. 10, 189--202 (2000; Zbl 0999.11040)]. For different average case results over all inversive sequences obtained by multiplying a fixed sequence with a nonzero constant see \textit{J. Eichenauer-Herrmann} and \textit{F. Emmerich} [Math. Comput. 65, 215--225 (1996; Zbl 0852.11041)] and \textit{F. Emmerich} [Math. Comput. 71, 781--791 (2002; Zbl 0991.65004)].
scientific article; zbMATH DE number 1891461
scientific article