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:
“Adulthood is the ever-shrinking period between childhood and old age. It is the apparent aim of modern industrial societies to reduce this period to a minimum.”
—Thomas Szasz (b. 1920)
“It is as if, to every period of history, there corresponded a privileged age and a particular division of human life: “youth” is the privileged age of the seventeenth century, childhood of the nineteenth, adolescence of the twentieth.”
—Philippe Ariés (20th century)
“This [new] period of parenting is an intense one. Never will we know such responsibility, such productive and hard work, such potential for isolation in the caretaking role and such intimacy and close involvement in the growth and development of another human being.”
—Joan Sheingold Ditzion and Dennie Palmer (20th century)