zbMATH — the first resource for mathematics

Explicit digital inversive pseudorandom numbers. (English) Zbl 0990.65005
The author introduces a new algorithm, the explicit digital inversive method, for the generation of uniform pseudorandom numbers. In particular, the statistical independence properties of the corresponding pseudorandom sequences (over parts of the period) are studied. This leads to interesting discrepancy bounds which are proved via exponential sums applying classical Weil bound.

65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
Full Text: EuDML
[1] DRMOTA M.-TICHY R. F.: Sequences, Discrepancies and Applications. Lecture Notes in Math. 1651, Springer-Verlag, New York, 1997. · Zbl 0877.11043
[2] EICHENAUER-HERRMANN J.: Pseudorandom number generation by nonlinear methods. Internat. Statist. Rev. 63 (1995), 247-255. · Zbl 0840.65005
[3] EICHENAUER-HERRMANN J.-NIEDERREITER H.: Digital inversive pseudo-random numbers. ACM Trans. Model. Comput. Simul. 4 (1994), 339-349. · Zbl 0847.11038
[4] EMMERICH F.: Statistical independence properties of inversive pseudorandom vectors over parts of the period. ACM Trans. Model. Comput. Simul. 8 (1998), 140-152. · Zbl 0926.11055
[5] HELLEKALEK P.-LARCHER G.: Random and Quasi-Random Point Sets. Lectures Notes in Statist. 138, Springer-Verlag, New York, 1998. · Zbl 0937.65004
[6] KOROBOV N. M.: Exponential Sums and Their Applications. Kluwer Academic Publishers, Dordrecht, 1992. · Zbl 0754.11022
[7] L’ECUYER P.: Uniform number generation. Ann. Oper. Res. 53 (1994), 77-120. · Zbl 0843.65004
[8] LEVIN M. B.: On the choice of parameters in generators of pseudorandom numbers. Sov. Math. Dokl 40 (1989), 101-105. · Zbl 0696.65003
[9] LIDL R.-NIEDERREITER H.: Finite Fields. Addison-Wesley, Reading, Mass., 1983. · Zbl 0554.12010
[10] MORENO, C J.-MORENO O.: Exponential sums and Goppa codes. I. Proc. Amer. Math. Soc. Ill (1991), 523-531. · Zbl 0716.94010
[11] NIEDERREITER H.: Pseudo-random numbers and optimal coefficients. Adv. Math. 26 (1977), 99-181. · Zbl 0366.65004
[12] NIEDERREITER H.: Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conf. Ser. in Appl. Math. 63, SIAM, Philadelphia, PA, 1992. · Zbl 0761.65002
[13] NIEDERREITER H.: Pseudorandom vector generation by the inversive method. AGM Trans. Model Comput. Simul. 4 (1994), 191-212. · Zbl 0847.11039
[14] NIEDERREITER H.: On a new class of pseudorandom numbers for simulation methods. J. Comput. Appl. Math. 56 (1994), 159-167. · Zbl 0823.65010
[15] NIEDERREITER H.-HELLEKALEK P.-LARCHER G.-ZINTERHOF P.: Monte Carlo and Quasi-Monte Carlo Methods 1996. Lectures Notes in Statist. 127, Springer-Verlag, New York, 1997. · Zbl 0879.00054
[16] TEZUKA S.: Uniform Random Numbers. Theory and Practice. Kluwer Academic Publishers, Dordrecht, 1995. · Zbl 0841.65004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.