Relations within sequences of congruential pseudo-random numbers
نویسندگان
چکیده
منابع مشابه
The Serial Test for Linear Congruential Pseudo-random Numbers
Let m>2 and r be integers, let y0 be an integer in the least residue system mod m, and let X be an integer coprime to m with X ^ ± 1 (mod m) and (X ~ l)y0 + r ^ 0 (mod m). A sequence y0,yl9...of integers in the least residue system mod m is generated by the recursion yn+ x = Xyn + r (mod m) for n = 0, 1, . . . . In the homogeneous case r = 0 (mod m), one chooses y0 to be coprime to m. The seque...
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The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method, both homogeneous and inhomogeneous, is estimated for parts of the period that are somewhat larger than the square root of the modulus. The analogous problem for an arbitrary linear congruential generator modulo a prime is also considered, the result being particularly interesting for maximal peri...
متن کاملOn the Distribution of Pseudo -Random Numbers Generated by the Linear Congruential Method. II
The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method is estimated for parts of the period which are somewhat larger than the square root of the modulus. Applications to numerical integration are mentioned.
متن کاملOn the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method
The discrepancy of sequences of pseudo-random numbers generated by the linear congruential method is estimated, thereby improving a result of Jagerman. Applications to numerical integration are mentioned. Let m be a modulus with primitive root X, and let y0 be an integer in the least residue system modulo m with g.c.d.(y0, m) = 1. We generate a sequence y0, yu of integers in the least residue s...
متن کاملThe Period of Pseudo-Random Numbers Generated by Lehmer's Congruential Method
It is well known that a sequence of randon numbers may be generated by Lehmer's congruential method. This method was originally executed in the formula; x n+1=23xn (mod 108+1). The period of this sequence eomes up to 5, 882, 352 which seems to be sufficient for almost all of our applications. The purpose of this paper is to provide an elementary method to account such a period of pseudo-random ...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
سال: 1969
ISSN: 0098-8979
DOI: 10.6028/jres.073b.005