Improving the domain of parameters for Newton's method with applications

Abstract

We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are weaker, the error bounds are tighter and the information on the location of the solution is at least as precise as in earlier studies. Numerical examples are given showing that our results apply to solve nonlinear equations in cases where the old results cannot apply.