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Gauss-Seidelization of iterative methods for solving ...

The Gauss-Seidelization of iterative methods for solvingnonlinear equations in the complex plane Jos e Manuel Guti errez, Angel Alberto Magre n an and Juan Luis Varona Dpto. de Matem aticas y Computaci on, Universidad de La Rioja, 26004 Logro no, to the memory of Professor Sergio PlazaAbstractIn this paper we introduce a process we have called Gauss-Seidelization for solving nonlinear equa-tions. We have used this name because the process is inspired by the well-known Gauss-Seidel methodto numerically solve a system of linear equations. Together with some convergence results, we presentseveral numerical experiments in order to emphasize how the Gauss-Seidelization process influences onthe dynamical behavior of an iterative method for solving nonlinear Subject Classification (2010):Primary 65H05; Secondary 28A78, :Nonlinear equations, iterative methods , Box-counting dimension, IntroductionLet us suppose that we want to solve the linear system{ax+by= ,cx+dy= ,(1)wherea,b,c,d, , are fixed real constants.}

The \Gauss-Seidelization" of iterative methods for solving nonlinear equations in the complex plane Jos e Manuel Guti errez, Angel Alberto Magren ~an and Juan Luis Varona y

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