Local convergence of inexact Newton-like iterative methods and applications

DOI10.1016/S0898-1221(99)00314-4zbMath0976.65054MaRDI QIDQ1975333

Ioannis K. Argyros

Publication date: 9 April 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

inexact Newton methodsBanach spacelocal convergencedifference Newton-like methodnonlinear autonomous first-order differential equationupdate-Newton methods

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (25)

On the Newton-Kantorovich hypothesis for solving equations ⋮ Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations ⋮ A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space ⋮ Weak sufficient convergence conditions and applications for Newton methods ⋮ On the convergence of Newton's method for a class of nonsmooth operators ⋮ Inexact Newton-type methods ⋮ On the semi-local convergence of Halley's method under a center-Lipschitz condition on the second Fréchet derivative ⋮ Approximate solution of the system of nonlinear integral equation by Newton-Kantorovich method ⋮ Local convergence of a secant type method for solving least squares problems ⋮ Sixth order derivative free family of iterative methods ⋮ Improved local convergence of Newton's method under weak majorant condition ⋮ An improved error analysis for Newton-like methods under generalized conditions ⋮ Extending the applicability of secant methods and nondiscrete induction ⋮ On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems. ⋮ Convergence of directional methods under mild differentiability and applications ⋮ Convergence radius of the modified Newton method for multiple zeros under Hölder continuous derivative ⋮ On the secant method for solving nonsmooth equations ⋮ On the midpoint method for solving equations ⋮ Extending the Newton-Kantorovich hypothesis for solving equations ⋮ Improved semi-local convergence of the Newton-HSS method for solving large systems of equations ⋮ Concerning the ``terra incognita between convergence regions of two Newton methods ⋮ Extending the applicability of the inexact Newton-HSS method for solving large systems of nonlinear equations ⋮ An Improved Convergence Analysis and Applications for Newton-Like Methods in Banach Space ⋮ On a class of Newton-like methods for solving nonlinear equations ⋮ On the semilocal convergence of inexact Newton methods in Banach spaces

Cites Work

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• A new semilocal convergence theorem for Newton's method
• Convergence of Newton-like-iterative methods
• On Q-order and R-order of convergence
• On the convergence of some projection methods with perturbation
• Relations between forcing sequences and inexact Newton iterates in Banach space
• Local Convergence of Inexact Newton Methods
• Inexact Newton Methods
• A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods

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