On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions

DOI10.1080/0020716021000059160zbMath1050.65056OpenAlexW2057979309MaRDI QIDQ4464418

Ioannis K. Argyros

Publication date: 27 May 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0020716021000059160

zbMATH Keywords

Newton's methodnumerical exampleserror boundsBanach spacenonlinear operator equationlocal convergenceFréchet-differentiable operatormajorizing sequenceHölder condition

Mathematics Subject Classification ID

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

Related Items (16)

Convergence radius of Osada's method under center-Hölder continuous condition ⋮ Improved estimates on majorizing sequences for the Newton-Kantorovich method ⋮ Unnamed Item ⋮ Convergence radius of Halley's method for multiple roots under center-Hölder continuous condition ⋮ A note on ``Convergence radius of Osada's method under Hölder continuous condition ⋮ On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems. ⋮ On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition ⋮ On a non-smooth version of Newton's method based on Hölderian assumptions ⋮ Convergence radius of the modified Newton method for multiple zeros under Hölder continuous derivative ⋮ Unnamed Item ⋮ General local convergence theory for a class of iterative processes and its applications to Newton's method ⋮ Convergence of Stirling's method under weak differentiability condition ⋮ Local convergence balls for nonlinear problems with multiplicity and their extension to eighth-order convergence ⋮ Estimating the radius of an attraction ball ⋮ An improved convergence analysis for the Newton–Kantorovich method using recurrence relations ⋮ An alternative analysis for the local convergence of iterative methods for multiple roots including when the multiplicity is unknown

Cites Work

• Unnamed Item
• A new semilocal convergence theorem for Newton's method
• Newton's method under mild differentiability conditions
• Newton's method under mild differentiability conditions with error analysis
• Local Convergence of Inexact Newton Methods
• On Newton's method and nondiscrete mathematical induction
• Accessibility Of Solutions By Newton's Method

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