Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers

• Autorzy: Jürgen Eichenauer-Herrmann , Harald Niederreiter
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 65
• Numer: 2
• Strony: 185-194

Daty

wydano

1993

otrzymano

1993-03-17

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, J. Lehn and A. Topuzoğlu, A nonlinear congruential pseudorandom number generator with power of two modulus, Math. Comp. 51 (1988), 757-759.
• [2] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
• [3] J. Eichenauer-Herrmann, On the autocorrelation structure of inversive congruential pseudorandom number sequences, Statist. Papers 33 (1992), 261-268.
• [4] J. Eichenauer-Herrmann, H. Grothe, H. Niederreiter and A. Topuzoğlu, On the lattice structure of a nonlinear generator with modulus $2^α$, J. Comput. Appl. Math. 31 (1990), 81-85.
• [5] J. Eichenauer-Herrmann and H. Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus, Math. Comp. 58 (1992), 775-779.
• [6] 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.
• [7] H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), 135-144.
• [8] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345.
• [9] H. Niederreiter, Nonlinear methods for pseudorandom number and vector generation, in: Simulation and Optimization, G. Pflug and U. Dieter (eds.), Lecture Notes in Economics and Math. Systems 374, Springer, Berlin, 1992, 145-153 .
• [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
• [11] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech., to appear.