Starting points for Newton's method under a center Lipschitz condition for the second derivative

DOI10.1016/j.cam.2016.12.013zbMath1478.65041OpenAlexW2562355363MaRDI QIDQ1676002

Ángel Alberto Magreñán, Miguel Ángel Hernández-Verón, José Antonio Ezquerro

Publication date: 3 November 2017

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.2016.12.013

zbMATH Keywords

error estimatesintegral equationNewton's methodsemilocal convergencemajorizing sequenceregion of accessibility

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (4)

On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces ⋮ Extending the domain of starting points for Newton's method under conditions on the second derivative ⋮ Mathematical modeling and computational methods ⋮ Semi-local convergence of a derivative-free method for solving equations

Cites Work

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• On the domain of starting points of Newton's method under center Lipschitz conditions
• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• Majorizing sequences for Newton's method from initial value problems
• A family of Halley-Chebyshev iterative schemes for non-Fréchet differentiable operators
• A convergence theorem for Newton-like methods in Banach spaces
• On the Newton-Kantorovich hypothesis for solving equations
• Newton's method under mild differentiability conditions with error analysis
• Third-order iterative methods under Kantorovich conditions
• Newton's method under weak Kantorovich conditions
• The Newton-Kantorovich Theorem

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