Abstract
We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted convergence regions in combination with majorizing scalar sequences and our technique of recurrent functions. Finally, a numerical example is given.
Reference13 articles.
1. Iterative Methods and Their Dynamics with Applications: A Contemporary Study;Argyros,2017
2. Numerical Methods for Unconstrained Optimization and Nonlinear Equations;Dennis,1983
3. Iterative Solution of Nonlinear Equations in Several Variables;Ortega,1970
4. On two high-order families of frozen Newton-type methods
5. On an efficient k-step iterative method for nonlinear equations