A new technique for studying the convergence of Newton’s solver with real life applications

The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to Kantorovich under variations of the convergence conditions. In this article, we use a different approach than before to increase the convergence domain, and without necessarily using conditions on the inverse of the Fréchet-derivative of the operator involved. Favorable to us applications are given to test the convergence criteria