A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
This paper is concerned with the problem of approximating a locally unique solution of the nonlinear equation \( F(x)+G(x) = 0 \), where \(F, G\) are operators defined on a closed ball \(\overline U (w,R)\) centered at point \(w\) and of radius \(R\geq 0\) which is a subset of a Banach space \(X\) with values in Banach space \(Y\). \(F\) is Fréchet-differentiable on \(\overline U (w,R)\), while the differentiability of the operator \(G\) is not assumed. The author provides a local as well as a semilocal convergence analysis for two-point Newton-like methods setting under very general Lipschitz type conditions. Several numerical examples are provided to show that author's results compare favorably with earlier ones.
scientific article; zbMATH DE number 2107273
scientific article