A NEW APPROACH TO SOLVE SYSTEMS OF LINEAR EQUATIONS

We propose a new iterative approach to solve systems of linear equations. The new strategy integrates the algebraic basis of the problem with elements horn classical mechanics all the finite difference method. The approach defines two families of convergent iterative methods. Each family is characterized by a linear differential equation, and every method is obtained from a suitable hoe difference scheme to integrate the associated dif ferential equation. The methods are general and depend on neither the matrix dimension nor the matrix structure. In this preliminary work, we present the basic features of the method with a simple application to a low dimensional system.