Improved generalized differentiability conditions for Newton-like methods

DOI10.1016/j.jco.2009.12.001zbMath1196.65100OpenAlexW2081284028MaRDI QIDQ983186

Saïd Hilout, Ioannis K. Argyros

Publication date: 3 August 2010

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2009.12.001

zbMATH Keywords

error estimatesnumerical examplesFréchet differentiable operatorsemilocal convergenceBanach spaceradiative transfernonlinear operator equationNewton-like methodsNewton-Kantorovich methodmajorizing sequenceChandrasekhar nonlinear integral equationdifferential equation with Green's kernel

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Nonlinear boundary value problems for ordinary differential equations (34B15) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (15)

Local convergence for multipoint methods using only the first derivative ⋮ A unifying theorem for Newton's method on spaces with a convergence structure ⋮ Local convergence analysis of the Gauss-Newton method under a majorant condition ⋮ On the local convergence of an eighth-order method for solving nonlinear equations ⋮ Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions ⋮ Semilocal convergence of a family of iterative methods in Banach spaces ⋮ Third-order Newton-type methods combined with vector extrapolation for solving nonlinear systems ⋮ Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ Newton-Kantorovich approximations under weak continuity conditions ⋮ Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions ⋮ Improved local convergence analysis of inexact Newton-like methods under the majorant condition ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ Local convergence analysis of inexact Gauss-Newton like methods under majorant condition ⋮ Accessibility of solutions of operator equations by Newton-like methods

Cites Work

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• A convergence theorem for Newton-like methods in Banach spaces
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• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Computational theory of iterative methods.
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence domains of certain iterative methods for solving nonlinear equations
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Generalized differentiability conditions for Newton's method
• A Unified Convergence Theory for a Class of Iterative Processes

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