A new semilocal convergence theorem for Newton's method involving twice Fréchet-differen\-tiabil\-ity at only one point

DOI10.1016/J.CAM.2004.12.005zbMath1075.65081OpenAlexW2052766026MaRDI QIDQ557695

Zhongyong Hu

Publication date: 30 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.12.005

zbMATH Keywords

numerical exampleerror estimatesNewton's methodsemilocal convergenceBanach spacenonlinear operator equationFréchet-differentiability

Mathematics Subject Classification ID

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

Cites Work

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• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• The theory of Newton's method
• On a theorem of L.V. Kantorovich concerning Newton's method.
• Newton's method under mild differentiability conditions with error analysis
• Accessibility Of Solutions By Newton's Method
• A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative
• A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer

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