A qualitative analysis of a family of newton-like iterative process with R-order of convergence at least three

Abstract

This work is focused on the study of iterative processes with R-order at least three in Banach spaces. We begin analyzing the semilocal convergence of a family of Newton-like iterative process. The most known iterative processes with R-order of convergence at least three are included in this family. In the study of iterative processes, there are two important points to bear in mind: the accessibility, which is analyzed by the convergence conditions required by the iterative process and the efficiency, which depends on the order of convergence and the operational cost in each step. These concepts are analyzed for the family of Newton-like iterative process. We obtain significant improvements from the study performed. Finally, considerations about the family of iterative processes are done and some numerical examples and applications to boundary-value problem are given.