On the effect of the multidimensional weight functions on the stability of iterative processes

Abstract

In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family is carried out on polynomial systems by selecting different weight functions and comparing the results obtained in each case. This study shows the applicability of the multidimensional dynamical analysis in order to select the methods of the family with the best stability properties.