Newton-Raphson method and arithmetic mean Newton’s method for weighted linear complementarity problems

Abstract

The goal of this thesis is to solve weighted linear complementarity problems. To do this, we first formulate the latter in the form of an equivalent system of nonlinear equations. We then applied the Newton-Raphson method to solve it. Under certain conditions, we prove the local quadratic convergence of this method to the unique solution. The numerical results obtained confirm the effectiveness of this method. Furthermore, to accelerate the convergence and improve the first method, we introduce the Newton arithmetic mean method. The numerical results obtained are very encouraging. Finally, we end this thesis with a conclusion and perspectives.