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A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative. (English) Zbl 0981.65067
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:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)