Improving point selection in cubature by a new discrepancy (Q2870637)

The discrepancy of a point set is used to measure the quality of a point set in cubature formulae. The authors generalize the F-discrepancy method of evaluating the uniformity of a point set to EF-discrepancy, which considers non-uniform distributions of points, assigning probabilities by partitioning using Voronoi cells, and the GF-discrepancy, which uses marginal F-discrepancies. The authors prove an extension of the Koksma-Hlawka (K-H) inequality for the EF-discrepancy, and give a conjecture of an extension of the K-H inequality for the GF-discrepancy. Numerical examples of the EF- and GF-discrepancy are given.NEWLINENEWLINE The authors also consider an application of GF-discrepancy to finding the optimal angles in RQ-SPM (rotational quasi-symmetric point method). Numerical examples are given in this direction.