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Zbl 0981.65067
Argyros, I.K.
A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative. (English)
[J] Comput. Math. Appl. 37, No.7, 109-115 (1999). ISSN 0898-1221

Summary: 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 Fréchet-derivative. Our results differ from earlier results in that we use Lipschitz conditions on the second Fréchet-derivative of the operator involved. Finally, we consider some particular situations to which our general results apply.

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: inexact Newton methods; Banach space; Fréchet-derivative; nonlinear equation; Lipschitz conditions

Cited in: Zbl pre05559068

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