On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses

DOI10.2478/s12175-013-0123-4zbMath1349.65183OpenAlexW2087034358MaRDI QIDQ2843889

Saïd Hilout, Ioannis K. Argyros

Publication date: 26 August 2013

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s12175-013-0123-4

zbMATH Keywords

numerical exampleNewton's methodsemilocal convergenceBanach spacelocal convergenceLipschitz conditionmajorizing sequencescenter-Lipschitz condition

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (2)

On the domain of starting points of Newton's method under center Lipschitz conditions ⋮ Enlarging the domain of starting points for Newton's method under center conditions on the first Fréchet-derivative

Cites Work

• General local convergence theory for a class of iterative processes and its applications to Newton's method
• Kantorovich-type convergence criterion for inexact Newton methods
• A convergence theorem for Newton-like methods in Banach spaces
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• A semilocal convergence analysis for directional Newton methods
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence domains of certain iterative methods for solving nonlinear equations
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• A Unified Convergence Theory for a Class of Iterative Processes

This page was built for publication: On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses