A Convergence Analysis for Directional Newton-like Methods

摘要

A semilocal convergence analysis for directional Newton-like methods in n-variables containing non-differentiable terms is provided in this study, using our new idea of recurrent functions. In the special case of Newton's method, our convergence analysis has the following advantages over the earlier work [8]: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and atleat a precise information on the location of the zero of the function. A numerical example where our results apply but others fail is also provided in this study.