Inversive Congruential Pseudorandom Numbers Avoid the Planes
نویسنده
چکیده
Nonlinear congruential pseudorandom number generators based on inversions have recently been introduced and analyzed. These generators do not show the lattice structure of the widely used linear congruential method. In the present paper it is proved that the points formed by d consecutive pseudorandom numbers of an inversive congruential generator with prime modulus possess an even stronger property: Any hyperplane in (/-space contains at most d of these points, that is to say, the hyperplane spanned by d arbitrary points of an inversive congruential generator contains no further points. This feature makes the inversive congruential method particularly attractive for simulation problems where linear structures within the generated points should be avoided.
منابع مشابه
Pseudorandom Number Generation by Inversive Methods
The classical linear congruential method for generating uniform pseudorandom numbers has some deficiencies that can render them useless for some simulation problems. This fact motivated the design and analysis of nonlinear congruential methods for the generation of pseudorandom numbers. Inversive methods are an interesting and very promising approach to produce uniform pseudorandom numbers. We ...
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