Obviating the bin width effect of the 1/t algorithm for multidimensional numerical integration

摘要

In this work we improve the accuracy and the convergence of the 1/t algorithm for multidimensional numerical integration. The proposed strategy is to introduce a new approximation method which obviates the bin width effect of the conventional 1/t algorithm by using the average of y values, which varies as the number of Monte Carlo trials changes, instead of the fixed value of y. The non-convergence of the 1/t algorithm and the convergence of the new method are proved by theoretical analysis. The potential of the method is illustrated by the evaluation of one-, two- and multi- dimensional integrals up to six dimensions. Our results show that the numerical estimates from our method converge to their exact values without either error saturation or the bin with effect, in contrast with the conventional 1/t algorithm.