Improving the rejection sampling method in quasi-Monte Carlo methods
The authors investigate and improve the performance of the deterministic rejection method in quasi-Monte Carlo (QMC) methods. They study the quality of the point sets generated by the standard deterministic rejection method. It turns out that the quality is closely related to the problem of QMC integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. Further on, in a rather general case, a method of smoothing characteristic functions is proposed. The characteristic functions are replaced by continuous ones, which have the same value of integral. This smoothing method is used to improve the rejection method. An extended smoothed version is described and numerical experiments are given.
scientific article; zbMATH DE number 1419819