Relaxed secant-type methods

Abstract

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our convergence criteria can be: weaker; the error bounds more precise and the convergence balls larger than in earlier studies \cite{18}-\cite{60}. Numerical examples are also presented to illustrate the theoretical results obtained in this study.