On the local convergence of a third order family of iterative processes (Q1736740)

Summary: Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect to consider is the accessibility of the iterative process, which shows the domain of starting points from which the iterative process converges to a solution of the equation. So, we consider a family of iterative processes with a higher efficiency index than Newton's method. However, this family of proecsses presents problems of accessibility to the solution \(x^\ast\). From a local study of the convergence of this family, we perform an optimization study of the accessibility and obtain iterative processes with better accessibility than Newton's method.