On a new class of inversive pseudorandom numbers for parallelized simulation methods
Tóm tắt
Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the digital explicit inversive method recently introduced by the authors. We establish some new results on the statistical properties of parallel streams of pseudorandom numbers generated by this method. In particular, we extend the results of the first author on the statistical properties of pseudorandom numbers generated by the explicit inversive congruential method introduced by Eichenauer-Herrmann. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties.
Tài liệu tham khảo
J. Eichenauer-Herrmann, Statistical independence of a new class of inversive congruential pseudorandom numbers, Math. Comp. 60 (1993), 375–384.
P. Hellekalek, General discrepancy estimates: the Walsh function system, Acta Arith. 67 (1994), 209–218.
R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge University Press, Cambridge, 1994.
G. Marsaglia, The structure of linear congruential sequences, in Applications of Number Theory to Numerical Analysis (S. K. Zaremba, Ed.), 249–285, Academic Press, New York, 1972.
C. J. Moreno and O. Moreno, Exponential sums and Goppa codes: I, Proc. Amer. Math. Soc. 111 (1991), 523–531.
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
H. Niederreiter, On a new class of pseudorandom numbers for simulation methods, J. Comp. Appl. Math. 56 (1994), 159–167.
H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225–240.
H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, Math. Comp., to appear.
H. Niederreiter and I. E. Shparlinski, On the distribution and lattice structure of nonlinear congruential pseudorandom numbers, Finite Fields Appl. 5 (1999), 246–253.
H. Niederreiter and I. E. Shparlinski, On the distribution of pseudorandom numbers and vectors generated by inversive methods, Appl. Algebra Engrg. Comm. Comput. 10 (2000), 189–202.
H. Niederreiter and A. Winterhof, Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators, Acta Arith. 93 (2000), 387–399.
H. Niederreiter and A. Winterhof, On the lattice structure of pseudorandom numbers generated over arbitrary finite fields, Preprint, 1999.