Kantorovich-type semilocal convergence analysis for inexact Newton methods

DOI10.1016/j.cam.2010.12.020zbMath1216.65065OpenAlexW2046576267MaRDI QIDQ631901

Hongmin Ren, Ioannis K. Argyros

Publication date: 14 March 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.12.020

zbMATH Keywords

Banach spacesnumerical examplessemilocal convergencenonlinear operator equationinexact Newton methodKantorovich majorazing sequenceLipschitz-center condition

Mathematics Subject Classification ID

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

Cites Work

• Local convergence of inexact methods under the Hölder condition
• Convergence criterion of inexact methods for operators with Hölder continuous derivatives
• On the semilocal convergence of inexact Newton methods in Banach spaces
• Kantorovich-type convergence criterion for inexact Newton methods
• The inexact Newton-like method for inverse eigenvalue problem
• On an application of Newton's method to nonlinear operators with \(\omega\)-conditioned second derivative
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative
• Computational theory of iterative methods.
• Local Convergence of Inexact Newton Methods
• Inexact Newton Methods
• Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results
• Generalized differentiability conditions for Newton's method
• On a two-point Newton-like method of convergent order two
• Matrix-Free Methods for Stiff Systems of ODE’s
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