Matrices and the structure of random number sequences
作者： George Marsaglia , Liang-Huei Tsay
DOI: 10.1016/0024-3795(85)90192-2
关键词:
摘要: Abstract This note provides a short, self-contained treatment, using linear algebra and matrix theory, for establishing maximal periods, underlying structure, choice of starting values shift-register lagged-Fibonacci random number generators.
core.ac.uk
elsevier.com
sci-hub.se 参考文章(11)
GEORGE MARSAGLIA, The Structure of Linear Congruential Sequences Applications of Number Theory to Numerical Analysis. pp. 249- 285 ,(1972) , 10.1016/B978-0-12-775950-0.50013-3
Donald E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms ,(1981)
M. Fushimi, S. Tezuka, The
k
-distribution of generalized feedback shift register pseudorandom numbers Communications of the ACM. ,vol. 26, pp. 516- 523 ,(1983) , 10.1145/358150.358159
T. G. Lewis, W. H. Payne, Generalized Feedback Shift Register Pseudorandom Number Algorithm Journal of the ACM. ,vol. 20, pp. 456- 468 ,(1973) , 10.1145/321765.321777
Jay P. Fillmore, Morris L. Marx, Linear Recursive Sequences Siam Review. ,vol. 10, pp. 342- 353 ,(1968) , 10.1137/1010059
John RB Whittlesey, Letters to the editor: on the multidimensional uniformity of pseudorandom generators Communications of The ACM. ,vol. 12, pp. 247- ,(1969) , 10.1145/362946.362949
Morgan Ward, The arithmetical theory of linear recurring series Transactions of the American Mathematical Society. ,vol. 35, pp. 600- 628 ,(1933) , 10.1090/S0002-9947-1933-1501705-4
G. Marsaglia, RANDOM NUMBERS FALL MAINLY IN THE PLANES Proceedings of the National Academy of Sciences of the United States of America. ,vol. 61, pp. 25- 28 ,(1968) , 10.1073/PNAS.61.1.25
Donald Ervin Knuth, The Art of Computer Programming ,(1968)
A. C. Arvillias, D. G. Maritsas, Partitioning the Period of a Class of
m
-Sequences and Application to Pseudorandom Number Generation Journal of the ACM. ,vol. 25, pp. 675- 686 ,(1978) , 10.1145/322092.322106