Period
The sequence must have after finitely many steps and since the next element depends only on its direct predecessor also etc. The maximum length that the period T for a function modulo q can have is T=q. If the polynomial (polynomial ring over ) is primitive, then the sequence will have the maximum length. Such polynomials are called inversive maximal period (IMP) polynomials. The sufficient condition for maximum sequence period is a proper choice of parameters a and c according to the algorithm described in. Eichenauer-Herrmann, Lehn, Grothe and Niederreiter have shown that inversive congruential generators have good uniformity properties, in particular with regard to lattice structure and serial correlations.
Read more about this topic: Inversive Congruential Generator
Famous quotes containing the word period:
“When we suffer anguish we return to early childhood because that is the period in which we first learnt to suffer the experience of total loss. It was more than that. It was the period in which we suffered more total losses than in all the rest of our life put together.”
—John Berger (b. 1926)