RNG
Papers to Be Read and Reviewed
- G. Marsaglia, "A
current view of random number generators," in Computing
Science and Statistics: Proceedings of the XVIth Symposium on the
Interface, pp. 3-10, 1985. (Hayles)
- D. E. Knuth, The
Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Third
Edition, Addison-Wesley, Reading, Massachusetts,
1998. (pages 1-41). (Zhao)
- P. L'Ecuyer, "Random
numbers for simulation," Communications
of the ACM, 33:85-97,
1990. (Sanal)
- A. M. Ferrenberg
and D. P. Landau and Y. J. Wong, "Monte
Carlo simulations: Hidden errors from `good' random number generators," Phys.
Rev. Let., 69:
3382-3384, 1992. (Whaley)
- R. C. Tausworthe, "Random
numbers generated by linear recurrence modulo two," Math.
Comput., 19:
201-209, 1965. (Chillumuntala)
- M. Matsumoto and Y.
Kurita, "Twisted
GFSR generators," ACM Transactions on Modeling and Computer Simulation, 2:
179-194, 1992. (Qiu)
- M. Matsumoto and T.
Nishimura, "Mersenne
twister: A 623-dimensionally equidistributed uniform pseudo-random
number generator," ACM Transactions on Modeling and Computer Simulation, 8: 3-30, 1998. (Ravindranath)
- F. Panneton, P.
L'Ecuyer, and M. Matsumoto, "Improved
Long-Period Generators Based on Linear Recurrences Modulo 2," ACM
Transactions on Mathematical Software,32(1):
1-16, 2006. (Lin)
- G. Marsaglia, "Random
numbers fall mainly in the planes," Proc.
Nat. Acad. Sci. U.S.A., 62:
25-28, 1968. (Zhu)
- J.
Eichenauer-Herrmann, "Inversive
congruential pseudorandom numbers avoid the planes," Math.
Comput., 56:
297-301, 1991. (Li)
- J.
Eichenauer-Herrmann, "Pseudorandom
generation by nonlinear methods," International
Statistical Review, 63:
247-255, 1995. (Cai)
- I. M. Soboĺ, "On
the distribution of points in a cube and the approximate evaluation of
integrals," U.S.S.R.
Computational Mathematics and Mathematical Physics, 7(4):
86-112, 1967. (Lin)
- W. J. Morokoff and
R. E. Caflisch, "Quasi-random
sequences and their discrepancies," SIAM Journal on
Scientific Computing, 15(6):
1251-1279, 1994. (Zhou)
- S. K. Zaremba, "The
mathematical basis of Monte Carlo and quasi-Monte Carlo methods," SIAM
Rev., 10: 303–314, 1968. (Zhang)
- K. F. Roth, "On irregularities of
distribution," Mathematika, 1: 73-79, 1954. (Zhao)
- A. B. Owen, "Randomly Permuted
(t,m,s)-Nets and (t,s)-Sequences", Lecture Notes in Statistics,
106: 299-317, 1995. (Lin)
- S. Tezuka, "Quasi-Monte Carlo-Discrepancy between theory and practice," in: K.T. Fang, F. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer-Verlag, Berlin, pp. 124-140, 2002. (Li)
- S. Tezuka and G.
Faure, "I-binomial
scrambling of digital nets and sequences," Journal
of Complexity, 19:
744-757, 2003. (Zhang)
- S. A. Smolyak, "Quadrature and interpolation formulas for tensor products of certain classes of functions," Dolk. Akad.Nauk SSSR, 4: 240-243, 1964. (Ravindranath)
- B. C. Bromley, "Quasirandom number generator for parallel Monte Carlo algorithms," Journal of Parallel and Distributed Computing, 38: 101-104, 1996. (Zhou)
- P. Frederickson and R. Hiromoto and T.
L. Jordan and B. Smith and T. Warnock, "Pseudo-random trees in Monte
Carlo", Parallel Computing, 1:
175-180, 1984. (Whaley)
- O. E. Percus and M.
H. Kalos, "Random
number generators for MIMD parallel processors," J.
of Par. Distr. Comput., 6:
477-497, 1988. (Cai)
- A. De'Matteis and
S. Pagnutti, "Controlling
correlations in parallel Monte Carlo", Parallel
Computing, 21:
73-84, 1995. (Chillumuntala)
- M. Mascagni and A.
Srinivasan, "Parameterizing
Parallel Multiplicative Lagged-Fibonacci Generators," Parallel
Computing, 30:
899-916, 2004. (Qiu)
- J. C. Lagarias, "Pseudorandom numbers," Statistical Science, 8: 31-39, 1993. (Hayles)
- G. Marsaglia and A. Zaman, "A new
class of random number generators," The Annals of Applied
Probability, 1: 462-480, 1991. (Yun)
- S. Tezuka and P. L'Ecuyer and R.
Couture, "On
the lattice structure of the add-with-carry and subtract-with-borrow
random number generators," ACM Transactions on
Modeling and Computer Simulation, 3(4):
315-331, 1993. (Sanal)