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  • Digitale Medien  (3)
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  • Digitale Medien  (3)
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  • 1
    Digitale Medien
    Digitale Medien
    A multiple recursive non-linear congruential pseudo random number generator (1987)
    Springer
    Manuscripta mathematica 59 (1987), S. 331-346 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n≥0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n≥0, the sequence of non-negative integers with xN(n)≢0 (mod p). The non-linear generator is defined by zn≡xN(n)+1·x N(n) −1 (mod p), n≥0, where x N(n) −1 denotes the inverse element of xN(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length pr and all (p−1)r r-tupels (y1,...,yr) with 1≤y1,...,yr≤p are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2].
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01174798
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  • 2
    Digitale Medien
    Digitale Medien
    On Marsaglia's lattice test for pseudorandom numbers (1988)
    Springer
    Manuscripta mathematica 62 (1988), S. 245-248 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Nonlinear recursive congruential pseudorandom number generators with prime modulus and maximal period length are considered. Those generators are characterized which behave optimally with respect to Marsaglia's lattice test. An example for an extremely bad generator with this property is given, which demonstrates the weakness of this test.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01278982
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  • 3
    Digitale Medien
    Digitale Medien
    On the structure of quadratic congruential sequences (1987)
    Springer
    Manuscripta mathematica 58 (1987), S. 129-140 
    Details
    ISSN: 1432-1785
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Sequences of integers defined by a quadratic congruential formula are divided into non-overlapping subsequences of length d. The structure of the set of the resulting points in the d-dimensional Euclidean space Rd is studied. The analysis is restricted to the case of sequences with maximal period length since such sequences are of special interest in connection with pseudo random number generation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169087
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