Improved the Convergence of Iterative Methods for Solving Systems of Equations by Memetics Techniques

Abstract

This work proposes proposed a technique inspired by memetic algorithm (MA) to improve the convergence of iterative methods for solving systems of equations. In the first phase the system of equations is transformed into an optimization problem. In this first phase, a memetics technique -ie a double optimization, local and global- is used to determine an initial vector favorable to a rapid convergence. In the second phase the system of equations is solved using an iterative method with the initial vector obtained in the previous phase. One can say that it is a hybrid method of solving systems of equations, both linear and nonlinear. The experimental results obtained with conjugate gradient, preconditioned conjugate gradient, Newton, Chebyshev and Broyden methods, serial and parallel versions, recommend the proposed method.