Preface of the 'Advances in Numerical Methods for Solving Nonlinear Equations and Systems'

摘要

The design of iterative methods for approximating the solution of nonlinear equations or systems is an interesting task in numerical analysis and applied scientific branches. During the last years, numerous papers devoted to the mentioned iterative methods have appeared in several journals. The existence of an extensive literature on these iterative methods reveals that this topic is a dynamic branch of the numerical studies with interesting and promising applications (the study of dynamical models of chemical reactors, radioactive transfer, preliminary orbit determination, etc). The aim of this symposium is to share the new trends in the field of iterative methods for nonlinear problems. In the following, we will give in alphabetic order a brief description of the topics of research discussed. In J. A. Ezquerro, D. Gonzalez and M. A. Hernandez's contribution a generalization of the semilocal convergence conditions given by Kantorovich for Newton's method is made, so that Kantorovich's convergence conditions are relaxed in order to Newton's method can be applied for solving more equations. In this paper, majorizing sequences adapted for particular problems are constructed. In particular, the previous Kantorovich-type conditions are relaxed to facilitate the convergence, by requiring some conditions on the second Frechet-derivative of the operator F.