ArticleOriginal scientific text
Title
General discrepancy estimates II: the Haar function system
Authors 1
Affiliations
- Institut für Mathematik, Universität Salzburg, Hellbrunner Strasse 34, A-5020 Salzburg, Austria
Keywords
discrepancy, Walsh functions, Haar functions, pseudorandom number generators, quasi-Monte Carlo methods
Bibliography
- J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
- P. Hellekalek, General discrepancy estimates: the Walsh function system, this volume, 209-218.
- L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
- H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. in Math. 26 (1977), 99-181.
- H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041.
- H. Niederreiter, New methods for pseudorandom number and pseudorandom vector generation, in: Proc. 1992 Winter Simulation Conference (Arlington, Va., 1992), IEEE Press, Piscataway, N.J., 1992, 264-269.
- H. Niederreiter, On a new class of pseudorandom numbers for simulation methods, J. Comput. Appl. Math., to appear.
- H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
- F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series. An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990.
- I. M. Sobol', Multidimensional Quadrature Formulas and Haar Functions, Nauka, Moscow, 1969 (in Russian).
- I. M. Sobol' and O. V. Nuzhdin, A new measure of irregularity of distribution, J. Number Theory 39 (1991), 367-373.