ON THE CONVERGENCE OF NEWTON'S METHOD UNDER UNIFORM CONTINUITY CONDITIONS

Abstract

A new semilocal convergence analysis for Newton's method is developed under
uniformly continuity assumptions on the Fr{\'e}chet-derivative of the operator. It turns out
that our analysis has several advantages over earlier studies. For example, error bounds
derived in this work are ner than the known results in scientific literature [1, 3, 18, 24,
25, 27, 28, 31, 38, 40, 41, 43, 46, 48, 53, 54, 55] and, under the same or weaker sufficient
convergence conditions, our analysis provide at least as precise information on the location
of the solution. Numerical examples are also presented which further validate the developed
theoritical results.