Proving the convergence of a modified process of single-level iterative aggregation for matrices with a small norm

An iterative process is described for solution of a set of balance type linear equations. The method is a modified process known as a single-level iterative aggregation. In this modification an accurate solution of appropriate systems of lower dimensionality is replaced by approximate solutions by the method of simple iteration. If the norm of the matrix of the initial system is small enough the process is proved to converge to an accurate solution of the system with any number of the steps in the method of simple iteration.