✦ LIBER ✦

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

✍ Scribed by I.K. Argyros

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 312 KB
Volume: 37
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(99)00091-7

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✦ Synopsis

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&~het-derivative of the operator involved. Finally we consider some particular situations to which our general results apply.