Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points

Authors:
Peter Winker;Kai-Tai Fang
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1997

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Abstract

Efficient routines for multidimensional numerical integration are provided by quasi--Monte Carlo methods. These methods are based on evaluating 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 points the evaluation of discrepancy becomes infeasible. The use of the efficient multiple-purpose heuristic threshold-accepting offers the possibility to obtain at least good approximations to the discrepancy of a given set of points. This paper presents an implementation of the threshold-accepting heuristic, an assessment of its performance for some small examples, and results for larger sets of points with unknown discrepancy.