Convergence Theorem for Newton-Like Methods in Banach Spaces

摘要

A convergence theorem for Newton-like methods in Banach spaces is given, which improves results of Rheinboldt, Dennis, Miel and Moret and includes as a special case an updated version of the Kantorovich theorem for the Newton method given in previous papers. Error bounds obtained previously are also improved. This paper unifies the study of finding sharp error bounds for Newton-like methods under Kantorovich type assumptions. Keywords: Error estimates; Iterative solutions of nonlinear equations in Banach spaces. (Author)