Concerning the semilocal convergence of Newton's method and convex majorants

DOI10.1007/s12215-008-0024-5zbMath1176.65058OpenAlexW1976845824MaRDI QIDQ1032571

Ioannis K. Argyros

Publication date: 26 October 2009

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-008-0024-5

zbMATH Keywords

Newton's methodsemilocal convergenceBanach spaceFréchet-derivativeconvex majorant

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Error analysis and interval analysis (65G99)

Related Items (3)

Extending the applicability of the Gauss-Newton method for convex composite optimization using restricted convergence domains and average Lipschitz conditions ⋮ Improved local convergence of Newton's method under weak majorant condition ⋮ A family of Kurchatov-type methods and its stability

Cites Work

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• Kantorovich's majorants principle for Newton's method
• Newton method under weak Lipschitz continuous derivative in Banach spaces.
• The Kantorovich theorem and interior point methods
• On the Newton-Kantorovich hypothesis for solving equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Computational theory of iterative methods.
• Convergence of Newton’s method and inverse function theorem in Banach space
• New results on newton-kantorovich approximations with applications to nonlinear integral equations
• Accessibility Of Solutions By Newton's Method

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