Introduction and background: Newton-type methods, order of convergence, and optimality conjectures

Apuntes

Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc Full Length Article Maximally efficient damped composed Newton-type methods to solve nonlinear systems of equations Alicia Cordero a,∗ , Renso V. Rojas-Hiciano b , Juan R. Torregrosa a , Maria P. Vassileva c a Multidisciplinary Mathematics Institute, Universitat Politècnica de València, Camino de Vera, 46022-Valencia, Spain b Escuela de Ciencias Naturales y Exactas, Pontificia Universidad Católica Madre y Maestra, Sarasota Ave., 10109 Santo Domingo D.N., Dominican Republic c Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo, Los Próceres, 10602 Santo Domingo D.N., Dominican Republic A R T I C L E I N F O A B S T R A C T Keywords: Iterative method Nonlinear system Order of convergence Optimal method Cordero-Torregrosa’s conjecture Maximally efficient methods Ermakov’s hyperfamily The main contribution of this manuscript is to introduce to the scientific community the concept of maximally efficient damped composed Newton-type method and the design of two schemes of this class of orders four and six. It is obtained from a different and new ex...