Mathematical modeling for systems of large dimension through a modification of the method of iterative aggregation

Abstract

This article provides a new method for accelerating the convergence such that is a synthesis of two methods: Seidel method and an iterative method for solving a linear system of equations. Using a new method accelerating the convergence for various grades of operator equations allows to construct a sequence of approximations that more convergence to solve the operator equations. In this paper, the method allows to significantly speed up the process of convergence to the precise solution. There is an implementation of the resulting method and sufficient conditions of convergence