APPLICATION OF THRESHOLD-ACCEPTING TO THE EVALUATION OF THE DISCREPANCY OF A SET OF POINTS

Efficient routines for multidimensional numerical integration are prov ided by quasi-Monte Carlo methods. These methods are based on evaluati ng the integrand at a set of representative points of the integration area. A set may be called representative if it shows a low discrepancy . However, in dimensions higher than two and for a large number of poi nts the evaluation of discrepancy becomes infeasible. The use of the e fficient multiple-purpose heuristic threshold-accepting offers the pos sibility to obtain at least good approximations to the discrepancy of a given set of points. This paper presents an implementation of the th reshold-accepting heuristic, an assessment of its performance for some small examples, and results for larger sets of points with unknown di screpancy.