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:
“The easiest period in a crisis situation is actually the battle itself. The most difficult is the period of indecision—whether to fight or run away. And the most dangerous period is the aftermath. It is then, with all his resources spent and his guard down, that an individual must watch out for dulled reactions and faulty judgment.”
—Richard M. Nixon (1913–1995)
“... there has never been a period in history when there have been necessary killings which has not been instantly followed by a period when there have been unnecessary killings.”
—Rebecca West (1892–1983)
“His singing carried me back to the period of the discovery of America ... when Europeans first encountered the simple faith of the Indian. There was, indeed, a beautiful simplicity about it; nothing of the dark and savage, only the mild and infantile. The sentiments of humility and reverence chiefly were expressed.”
—Henry David Thoreau (1817–1862)