Journal article

Publication year: 1997

Pages: 2028-2042

Journal: SIAM Journal on Numerical Analysis

Volume number: 34

Issue number: 5

ISSN: 0036-1429

eISSN: 1095-7170

DOI Link: https://doi.org/10.1137/S0036142995286076

Publisher: Society for Industrial and Applied Mathematics

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.

Harvard Citation style: Winker, P. and Fang, K. (1997) Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points, SIAM Journal on Numerical Analysis, 34(5), pp. 2028-2042. https://doi.org/10.1137/S0036142995286076

APA Citation style: Winker, P., & Fang, K. (1997). Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points. SIAM Journal on Numerical Analysis. 34(5), 2028-2042. https://doi.org/10.1137/S0036142995286076