On the weakening of the convergence of Newton's method using recurrent functions

DOI10.1016/J.JCO.2009.06.003zbMath1259.65079OpenAlexW2038371069MaRDI QIDQ1049398

Saïd Hilout, Ioannis K. Argyros

Publication date: 12 January 2010

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2009.06.003

zbMATH Keywords

integral equationNewton's methodnumerical examplesdifferential equationHölder continuitysemilocal convergenceBanach spaceLipschitz continuityrecurrent functionsNewton-Kantorovich hypothesis

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (6)

Weaker convergence for Newton's method under Hölder differentiability ⋮ On the semilocal convergence of efficient Chebyshev-secant-type methods ⋮ Majorizing sequences for iterative procedures in Banach spaces ⋮ Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains ⋮ Improved generalized differentiability conditions for Newton-like methods ⋮ Efficient Steffensen-type algorithms for solving nonlinear equations

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• Convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement
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• On some methods of the approximate solution of nonlinear functional equations in Banach spaces
• Convergence and Applications of Newton-type Iterations
• New results on newton-kantorovich approximations with applications to nonlinear integral equations
• Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results

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