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:
“Of all the barbarous middle ages, that
Which is most barbarous is the middle age
Of man! it is—I really scarce know what;
But when we hover between fool and sage,
And don’t know justly what we would be at—
A period something like a printed page,
Black letter upon foolscap, while our hair
Grows grizzled, and we are not what we were.”
—George Gordon Noel Byron (1788–1824)
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—Augustus Y. Napier (20th century)
“There’s always a period of curious fear between the first sweet-smelling breeze and the time when the rain comes cracking down.”
—Don Delillo (b. 1926)