On the semilocal convergence of inexact Newton methods in Banach spaces

DOI10.1016/j.cam.2008.10.005zbMath1400.65029OpenAlexW1967307677MaRDI QIDQ1019815

Ioannis K. Argyros

Publication date: 28 May 2009

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.2008.10.005

zbMATH Keywords

semilocal convergenceBanach spaceresidualLipschitz conditioninexact Newton methodmajorizing sequencecenter-Lipschitz condition

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (9)

Semilocal convergence analysis for the modified Newton-HSS method under the Hölder condition ⋮ Robust semi-local convergence analysis for inexact Newton method ⋮ Improved local convergence analysis of inexact Gauss-Newton like methods under the majorant condition in Banach spaces ⋮ Improved local convergence of Newton's method under weak majorant condition ⋮ Kantorovich-type semilocal convergence analysis for inexact Newton methods ⋮ On the Gauss-Newton method ⋮ On the local convergence of inexact Newton-type methods under residual control-type conditions ⋮ Improved local convergence analysis of inexact Newton-like methods under the majorant condition ⋮ On the convergence of inexact two-step Newton-like algorithms using recurrent functions

Cites Work

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• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• Convergence on the iteration of Halley family in weak conditions
• A class of two-stage iterative methods for systems of weakly nonlinear equations
• Relations between forcing sequences and inexact Newton iterates in Banach space
• On the Newton-Kantorovich hypothesis for solving equations
• 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
• Forcing sequences and inexact Newton iterates in Banach space
• Local convergence of inexact Newton-like iterative methods and applications
• Local Convergence of Inexact Newton Methods
• Inexact Newton Methods

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