On the \(L_2\)-discrepancy for anchored boxes
The author considers the \(L_2\)-*discrepancy of a point set in a high-dimensional unit cube. He observes that the \(L_2\)-discrepancy is a quite bad gauge for uniform distribution if the number of points is not very large (depending on the dimension of the cube). Constructions of randomized point sets introduced by \textit{A. B. Owen} [SIAM J. Numer. Anal. 34, No.~5, 1884-1910 (1997; Zbl 0890.65023)] are modified, which allow very efficient implementations, and still satisfy discrepancy bounds as given by \textit{F. J. Hickernell} [ACM Trans. Model. Comput. Simul. 6, No.~4, 274-296 (1996; Zbl 0887.65030)]. The author also reports on numerical experiments. A bound for the \(L_2\)-discrepancy of an algorithm given recently by \textit{S. Heinrich} [Math. Comput. 65, No.~216, 1621-1633 (1996; Zbl 0853.65004)] is given.
scientific article; zbMATH DE number 1251399
scientific article