A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions

DOI10.1016/0096-3003(94)90144-9zbMath0796.65077OpenAlexW2033581615MaRDI QIDQ1320119

Ioannis K. Argyros

Publication date: 17 October 1994

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

Full work available at URL: https://doi.org/10.1016/0096-3003(94)90144-9

zbMATH Keywords

convergenceerror estimateBanach spaceNewton-like methodnonlinear operator equationmajorant method

Mathematics Subject Classification ID

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

Related Items (11)

On the Convergence of Secant-Like Methods ⋮ On a higher order secant method. ⋮ A modification of Newton's method for nondifferentiable equations. ⋮ Fixed points for operators with generalized Hölder derivative ⋮ A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer ⋮ New sufficient convergence conditions for the secant method ⋮ On a Newton-Kurchatov-type Iterative Process ⋮ Concerning the convergence of a modified Newton-like method ⋮ Convergence rates for inexact Newton-like methods at singular points and applications ⋮ On the convergence of a certain class of iterative procedures under relaxed conditions with applications ⋮ A uniparametric family of iterative processes for solving nondifferentiable equations

Cites Work

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• A convergence theorem for Newton-like methods in Banach spaces
• On the convergence of generalized Newton methods and implicit functions
• On a mesh-independence principle for operator equations and the secant method
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Newton-like methods under mild differentiability conditions with error analysis
• Convergence domains of certain iterative methods for solving nonlinear equations
• Sharp error bounds for Newton-like methods under weak smoothness assumptions
• On the application of the newton-kantorovich method to nonlinear integral equations of uryson type

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