[en] A cross factorization for the solution of the finite difference equation of the neutron diffusion equation is developed for the case of two and three dimensional spaces. In the method factorization is carried out along two directions (three directions in three dimensional case) in the network, and the method has been proved more advanced than the alternating method. The formulas of cross factorizations are derived for the case of two and three dimensional geometries, and the convergence of interaction and the method to determine parameter ω are investigated. (author)