From linear to nonlinear iterative methods

Abstract

This paper constitutes an effort towards the generalization of the most common classical iterative methods used for the solution of linear systems (like Gauss–Seidel, SOR, Jacobi, and others) to the solution of systems of nonlinear algebraic and/or transcendental equations, as well as to unconstrained optimization of nonlinear functions. Convergence and experimental results are presented. The proposed algorithms have also been implemented and tested on classical test problems and on real-life artificial neural network applications and the results to date appear to be very promising.