An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers

• Autorzy: Jürgen Eichenauer-Herrmann , Harald Niederreiter
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 2
• Strony: 193-198

Daty

wydano

1995

otrzymano

1994-07-18

Twórcy

autor

Jürgen Eichenauer-Herrmann

• Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, F.R.G.

autor

Harald Niederreiter

• Institut für Informationsverarbeitung, Österreichische Akademie, der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria

Bibliografia

• [1] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
• [2] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers, Z. Angew. Math. Mech. 73 (1993), T644-T647.
• [3] J. Eichenauer-Herrmann, Pseudorandom number generation by nonlinear methods, Internat. Statist. Rev., to appear.
• [4] J. Eichenauer-Herrmann and H. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), 243-249.
• [5] 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.
• [6] D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms , 2nd ed., Addison-Wesley, Reading, Mass., 1981.
• [7] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345.
• [8] H. Niederreiter, Nonlinear methods for pseudorandom number and vector generation, in: Simulation and Optimization, G. Pflug and U. Dieter (eds.), Lecture Notes in Econom. and Math. Systems 374, Springer, Berlin, 1992, 145-153.
• [9] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992.
• [10] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652