An adaptive Monte Carlo integration algorithm with general division approach

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The algorithm uses iteratively the idea of separating the domain of integration into 2^s$2^s$subregions. The proposed algorithm can be applied directly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional integral using a two-division approach. The numerical results show that the proposed algorithm gives better results than using one-division approach.