Resumen de Extended local and semilocal convergence for interpolatory iterative methods for nonlinear equations

Ioannis Karatzas, Stepan Shakhno, Halyna Yarmola

• Two iterative methods free of the Fréchet derivative of a nonlinear operator are considered. A local and a semilocal convergence analysis of the methods is carried out under Lipschitz conditions for the first-order divided differences and Hölder conditions for the second-order divided differences. The dependence of the convergence orders of methods on the Hölder constant and uniqueness ball are established. In this article we use our new idea of the restricted convergence region and present an improved convergence analysis of these methods. A numerical example, which demonstrates advantages of our approach to study convergence of iterative methods for solving nonlinear equations, is given.