On an improved convergence analysis of Newton's method

DOI10.1016/J.AMC.2013.09.049zbMath1336.65098OpenAlexW2041463299MaRDI QIDQ275758

Saïd Hilout, Ioannis K. Argyros

Publication date: 26 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.09.049

zbMATH Keywords

Newton's methodBanach spaceFréchet-derivativedivided difference of order oneKantorovich's hypothesissemi-local convergence

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15)

Related Items (8)

Directional \(k\)-step Newton methods in \(n\) variables and its semilocal convergence analysis ⋮ Convergence analysis of the Gauss-Newton-Potra method for nonlinear least squares problems ⋮ Unnamed Item ⋮ Extending the applicability of the local and semilocal convergence of Newton's method ⋮ Unified convergence domains of Newton-like methods for solving operator equations ⋮ Improving the domain of parameters for Newton's method with applications ⋮ Predetermining the number of periodic steps in multi-step Newton-like methods for solving equations and systems of equations ⋮ Weaker convergence criteria for Traub's method

Uses Software

• NewtonLib

Cites Work

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• Weaker conditions for the convergence of Newton's method
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• A convergence theorem for Newton-like methods in Banach spaces
• Estimating upper bounds on the limit points of majorizing sequences for Newton's method
• Computational theory of iterative methods.
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Computational Methods in Nonlinear Analysis
• 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
• Convergence and Complexity of Newton Iteration for Operator Equations
• Adaptive Approximation of Nonlinear Operators
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• The inexact, inexact perturbed, and quasi-Newton methods are equivalent models

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