On the convergence of inexact Newton-like methods under mild differentiability conditions

DOI10.1016/j.amc.2019.124871zbMath1433.65103OpenAlexW2991556579WikidataQ126649778 ScholiaQ126649778MaRDI QIDQ2287611

Vipin Kumar Singh

Publication date: 21 January 2020

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

Full work available at URL: https://doi.org/10.1016/j.amc.2019.124871

zbMATH Keywords

Fréchet derivativenonlinear operator equationNewton-Kantorovich methodinexact Newton's method and Fredholm integral equation

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

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Cites Work

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• Expanding the applicability of inexact Newton methods under Smale's (\(\alpha\), \(\gamma\))-theory
• Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space
• Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces
• A Newton-like method for generalized operator equations in Banach spaces
• Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces
• Majorizing sequences for Newton's method from initial value problems
• On dominating sequence method in the point estimate and Smale's theorem
• Local convergence of inexact methods under the Hölder condition
• Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition
• Improved generalized differentiability conditions for Newton-like methods
• Kantorovich-type convergence criterion for inexact Newton methods
• On the convergence of Newton-type methods under mild differentiability conditions
• On Newton's method under mild differentiability conditions and applications
• An improved error analysis for Newton-like methods under generalized conditions
• A modification of the classic conditions of Newton-Kantorovich for Newton's method
• Majorizing sequences for iterative methods
• A semilocal convergence result for Newton's method under generalized conditions of Kantorovich
• The convergence ball of Newton-like methods in Banach space and applications
• Convergence behaviour of inexact Newton methods under weak Lipschitz condition.
• An extension of a theorem by Wang for Smale's \(\alpha\)-theory and applications
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Expanding the applicability of inexact Newton methods using restricted convergence domains
• Local Convergence of Inexact Newton Methods
• Inexact Newton Methods
• Convergence of Newton’s method and inverse function theorem in Banach space
• Convergence behaviour of inexact Newton methods
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space
• The Kantorovich Theorem for Newton's Method

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