On the radius of convergence of Newton's method under average mild differentiability conditions

DOI10.1007/S12190-008-0143-3zbMath1184.65059OpenAlexW2069891731MaRDI QIDQ1032563

Ioannis K. Argyros

Publication date: 26 October 2009

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

Full work available at URL: https://doi.org/10.1007/s12190-008-0143-3

zbMATH Keywords

Newton's methodnumerical examplesHölder continuityBanach spacelocal convergenceFréchet-derivativeradius of convergence

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• On Newton's method under mild differentiability conditions and applications
• The convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivatives
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space

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