A semilocal convergence analysis for directional Newton methods

A semilocal convergence analysis for directional Newton methods in n-variables is provided in this study. Using weaker hypotheses than in the elegant related work by Y. Levin and A. Ben-Israel and introducing the center-Lipschitz condition we provide under the same computational cost as in Levin and Ben-Israel a semilocal convergence analysis with the following advantages: weaker convergence conditions; larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the zero of the function. A numerical example where our results apply to solve an equation but not the ones in Levin and Ben-Israel is also provided in this study.