Majorizing sequences for Newton's method from initial value problems

DOI10.1016/j.cam.2011.11.012zbMath1241.65051OpenAlexW2090697352MaRDI QIDQ765273

D. González, Miguel A. Hernández, José Antonio Ezquerro

Publication date: 19 March 2012

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.2011.11.012

zbMATH Keywords

Newton's methodsemilocal convergenceBanach spacenonlinear operator equationorder of convergencemajorizing sequenceBratu equationKantorovich's technique

Mathematics Subject Classification ID

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

Related Items (18)

Extending the domain of starting points for Newton's method under conditions on the second derivative ⋮ Extended iterative schemes based on decomposition for nonlinear models ⋮ On a result by Dennis and Schnabel for Newton's method: further improvements ⋮ A study on the local convergence and complex dynamics of Kou's family of iterative methods ⋮ On the existence of solutions of nonlinear Fredholm integral equations from Kantorovich's technique ⋮ Starting points for Newton's method under a center Lipschitz condition for the second derivative ⋮ On a two-step optimal Steffensen-type method: relaxed local and semi-local convergence analysis and dynamical stability ⋮ An improvement of derivative-free point-to-point iterative processes with central divided differences ⋮ Auxiliary point on the semilocal convergence of Newton's method ⋮ A semilocal convergence result for Newton's method under generalized conditions of Kantorovich ⋮ Extending the applicability of Newton's method for \(k\)-Fréchet differentiable operators in Banach spaces ⋮ Extending the applicability of Newton's method by improving a local result due to Dennis and Schnabel ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ Center conditions on high order derivatives in the semilocal convergence of Newton's method ⋮ Majorizing sequences for Newton's method under centred conditions for the derivative ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ On the complexity of choosing majorizing sequences for iterative procedures ⋮ The Theory of Kantorovich for Newton’s Method: Conditions on the Second Derivative

Cites Work

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• Dynamics of the solution of Bratu's equation
• Halley's method for operators with unbounded second derivative
• A convergence theorem for Newton-like methods in Banach spaces
• Sharp error bounds for Newton's process
• On the Newton-Kantorovich hypothesis for solving equations
• An Improved Convergence Analysis and Applications for Newton-Like Methods in Banach Space
• A Unified Convergence Theory for a Class of Iterative Processes

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