On Convergence Domains of Newton's and Modified Newton Methods

DOI10.1081/NFA-200067300zbMath1077.65057OpenAlexW2075040798MaRDI QIDQ5466751

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Publication date: 25 August 2005

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-200067300

zbMATH Keywords

convergenceerror boundsBanach spaceNewton methodnonlinear operator equationsmodified Newton method\(\omega\)-smoothnessregular smoothness

Mathematics Subject Classification ID

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

Related Items (6)

On a class of systems of difference equations and their invariants ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ Secant method with regularly continuous divided differences ⋮ Modified Ishikawa Iteration Process for Nonlinear Lipschitz Generalized Strongly Pseudo-Contractive Operators in Arbitrary Banach Spaces ⋮ Optimal Iterative Methods for Nonlinear Equations ⋮ Ulm's method without derivatives

Cites Work

• Unnamed Item
• Newton's method under a weak smoothness assumption
• Convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement
• Regular smoothness and newton' method
• Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results
• Kantorovich's Majorization and Functional Equations
• Newton—type methods under regular smoothness

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