Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains

DOI10.1007/S10910-016-0720-XzbMath1387.65050OpenAlexW2564862838MaRDI QIDQ683872

Ioannis K. Argyros, José Antonio Ezquerro, Miguel Ángel Hernández-Verón, Ángel Alberto Magreñán

Publication date: 9 February 2018

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-016-0720-x

zbMATH Keywords

semilocal convergenceNewton methodVertgeim conditions

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• On the weakening of the convergence of Newton's method using recurrent functions
• Convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement
• Concerning the ``terra incognita between convergence regions of two Newton methods
• Newton's method under mild differentiability conditions with error analysis
• Families of Newton-like methods with fourth-order convergence
• On some methods of the approximate solution of nonlinear functional equations in Banach spaces
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results
• The Newton-Kantorovich Theorem
• The Newton method for operators with Hölder continuous first derivative
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