Construction of Equidistributed Generators Based on Linear Recurrences Modulo 2

Random number generators based on linear recurrences modulo 2 are widely used and appear in different forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Low-discrepancy point sets for quasi-Monte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by certain equidistribution criteria. Combining two or more recurrences and adding linear output transformations can be used to improve the equidistribution properties.

[1]  Pierre L'Ecuyer,et al.  A new class of linear feedback shift register generators , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[2]  P. L'Ecuyer,et al.  Uniform random number generators , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[3]  手塚 集.  Uniform random numbers : theory and practice , 1995 .

[4]  Makoto Matsumoto,et al.  Twisted GFSR generators II , 1994, TOMC.

[5]  Pierre L'Ecuyer,et al.  Random Number Generators: Selection Criteria and Testing , 1998 .

[6]  Pierre L'Ecuyer,et al.  Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation , 2001, SIAM J. Sci. Comput..

[7]  Pierre L'Ecuyer,et al.  Efficient and portable combined Tausworthe random number generators , 1990, TOMC.

[8]  Pierre L'Ecuyer,et al.  Maximally equidistributed combined Tausworthe generators , 1996, Math. Comput..

[9]  Makoto Matsumoto,et al.  Twisted GFSR generators , 1992, TOMC.

[10]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[11]  P. L’Ecuyer,et al.  On selection criteria for lattice rules and other quasi-Monte Carlo point sets , 2001 .

[12]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[13]  Pierre L'Ecuyer,et al.  Uniform random number generation , 1994, Ann. Oper. Res..

[14]  R. Tausworthe.  Random Numbers Generated by Linear Recurrence Modulo Two , 1965 .

[15]  Masanori Fushimi,et al.  Designing a Uniform Random Number Generator Whose Subsequences are k-Distributed , 1988, SIAM J. Comput..

[16]  P. L’Ecuyer,et al.  Variance Reduction via Lattice Rules , 1999 .

[17]  J. P. R. Tootill,et al.  An Asymptotically Random Tausworthe Sequence , 1973, JACM.

[18]  Pierre L'Ecuyer,et al.  Tables of maximally equidistributed combined LFSR generators , 1999, Math. Comput..

[19]  Masanori Fushimi.  Increasing the Orders of Equidistribution of the Leading Bits of the Tausworthe Sequence , 1983, Inf. Process. Lett..

[20]  Russell R. Barton,et al.  Proceedings of the 2000 winter simulation conference , 2000 .

[21]  Shu Tezuka,et al.  Uniform Random Numbers , 1995 .