DISCREPANCY-BASED ERROR-ESTIMATES FOR QUASI-MONTE CARLO .2. RESULTS IN ONE-DIMENSION

The choice of a point set, to be used in numerical integration, determ ines, to a large extent, the error estimate of the integral. Point set s can be characterized by their discrepancy, which is a measure of the ir nonuniformity. Point sets with a discrepancy that is low with respe ct to the expected value for truly random point sets, are generally th ought to be desirable. A low value of the discrepancy implies a negati ve correlation between the points, which may be usefully employed to i mprove the error estimate of a numerical integral based on the point s et. We apply the formalism developed in a previous publication to comp ute this correlation for one-dimensional point sets, using a few diffe rent definitions of discrepancy.