Explicit inversive congruential pseudorandom numbers with power of two modulus
HTML articles powered by AMS MathViewer
- by Jürgen Eichenauer-Herrmann and Katja Ickstadt PDF
- Math. Comp. 62 (1994), 787-797 Request permission
Abstract:
An explicit version of the inversive congruential method with power of two modulus for generating uniform pseudorandom numbers is introduced. Statistical independence properties of the generated sequences are studied by means of the serial test. The method of proof relies on a detailed analysis of certain exponential sums.References
- Jürgen Eichenauer and Jürgen Lehn, A nonlinear congruential pseudorandom number generator, Statist. Hefte 27 (1986), no. 4, 315–326. MR 877295
- Jürgen Eichenauer, Jürgen Lehn, and Alev Topuzoğlu, A nonlinear congruential pseudorandom number generator with power of two modulus, Math. Comp. 51 (1988), no. 184, 757–759. MR 958641, DOI 10.1090/S0025-5718-1988-0958641-1
- J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers, Z. Angew. Math. Mech. 73 (1993), no. 7-8, T644–T647. Bericht über die Wissenschaftliche Jahrestagung der GAMM (Leipzig, 1992). MR 1237851, DOI 10.2307/1403647 —, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
- Jürgen Eichenauer-Herrmann, Inversive congruential pseudorandom numbers avoid the planes, Math. Comp. 56 (1991), no. 193, 297–301. MR 1052092, DOI 10.1090/S0025-5718-1991-1052092-X
- J. Eichenauer-Herrmann, On the autocorrelation structure of inversive congruential pseudorandom number sequences, Statist. Papers 33 (1992), no. 3, 261–268. MR 1186171, DOI 10.1007/BF02925329
- Jürgen Eichenauer-Herrmann, Statistical independence of a new class of inversive congruential pseudorandom numbers, Math. Comp. 60 (1993), no. 201, 375–384. MR 1159168, DOI 10.1090/S0025-5718-1993-1159168-9
- J. Eichenauer-Herrmann, H. Grothe, H. Niederreiter, and A. Topuzoğlu, On the lattice structure of a nonlinear generator with modulus $2^\alpha$, J. Comput. Appl. Math. 31 (1990), no. 1, 81–85. Random numbers and simulation (Lambrecht, 1988). MR 1068151, DOI 10.1016/0377-0427(90)90338-Z
- Jürgen Eichenauer-Herrmann and Harald Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus, Math. Comp. 58 (1992), no. 198, 775–779. MR 1122066, DOI 10.1090/S0025-5718-1992-1122066-X
- Jürgen Eichenauer-Herrmann and Harald Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), no. 2, 243–249. MR 1107870, DOI 10.1016/0377-0427(91)90046-M
- Mary Flahive and Harald Niederreiter, On inversive congruential generators for pseudorandom numbers, Finite fields, coding theory, and advances in communications and computing (Las Vegas, NV, 1991) Lecture Notes in Pure and Appl. Math., vol. 141, Dekker, New York, 1993, pp. 75–80. MR 1199823
- J. Kiefer, On large deviations of the empiric D. F. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961), 649–660. MR 131885
- Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. MR 746963
- Harald Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), no. 185, 135–144. MR 971407, DOI 10.1090/S0025-5718-1989-0971407-2
- Harald Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers, Math. Comp. 55 (1990), no. 191, 277–287. MR 1023766, DOI 10.1090/S0025-5718-1990-1023766-0
- Harald Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), no. 1-4, 323–345. Stochastic programming, Part II (Ann Arbor, MI, 1989). MR 1118905, DOI 10.1007/BF02204856
- Harald Niederreiter, Finite fields and their applications, Contributions to general algebra, 7 (Vienna, 1990) Hölder-Pichler-Tempsky, Vienna, 1991, pp. 251–264. MR 1143089 —, Nonlinear methods for pseudorandom number and vector generation, Simulation and Optimization (G. Pflug and U. Dieter, eds.), Lecture Notes in Econom. and Math. Systems, vol. 374, Springer, Berlin, 1992, pp. 145-153.
- Harald Niederreiter, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1172997, DOI 10.1137/1.9781611970081
- Harald Niederreiter, Finite fields, pseudorandom numbers, and quasirandom points, Finite fields, coding theory, and advances in communications and computing (Las Vegas, NV, 1991) Lecture Notes in Pure and Appl. Math., vol. 141, Dekker, New York, 1993, pp. 375–394. MR 1199844 —, New methods for pseudorandom number and pseudorandom vector generation, Proc. 1992 Winter Simulation Conf. (Arlington, Va., 1992), IEEE Press, Piscataway, NJ, 1992, pp. 264-269.
- H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), no. 7-8, T648–T652. Bericht über die Wissenschaftliche Jahrestagung der GAMM (Leipzig, 1992). MR 1237852
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 62 (1994), 787-797
- MSC: Primary 11K45; Secondary 11K38, 65C10
- DOI: https://doi.org/10.1090/S0025-5718-1994-1212266-4
- MathSciNet review: 1212266