On the discrepancy of quadratic congruential pseudorandom numbers
Knuth's quadratic congruential method [\textit{D. E. Knuth}, The Art of Computer Programming, Vol. 2 (1981; Zbl 0477.65002)] is analysed to examine the statistical independence of consecutive pairs in the pseudorandom stream produced. The basic congruence is \[ y_{n+1}\equiv ay^ 2_ n+by_ n+c(mod p^ m)\quad (n\geq 0) \] and a,b,c are to have optimal properties. Inequality results are obtained for the appropriately described discrepancy measure and this enables a contrast to be made with the performance of the linear congruential method mod \(p^ m\).
statistical independence of consecutive pairs
scientific article; zbMATH DE number 4208183
scientific article