Semilocal Convergence Theorems for Newton’s Method Using Outer Inverses and Hypotheses on the Second Fréchet-Derivative

A new convergence theorem for the inexac

A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative

✍ I.K. Argyros 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 312 KB

We provide sufficient conditions for the convergence of inexact Newton methods to a solution of a nonlinear equation in a Banach space. Earlier results have used conditions on the first Fr&het-derivative. Our results differ from earlier results in that we use Lipschitz conditions on the second Fr&~h