By using results contained in [5] on the caracterization of natural L-spline functions, in this paper we will give a convenient general criterion for smoothing, in the successive approximation method, the solution of badly ill-conditioned linear least squares systems. Besided, for solving a special class of non linear algebraic systems (with properties a), b) and c) stated in § 3)), we shall present an efficient iterative method which has been generated by imposing particular conditions on the discrete dynamical systems associated to the given algebraic systems.