Semilocal Convergence Theorem for a Newton-like Method

DOI10.4208/eajam.090816.270317azbMath1383.65056OpenAlexW2751959998MaRDI QIDQ4605724

Lu Liu, Min-Hong Chen, Rongfei Lin, Ping-Fei Dai, Qing-Biao Wu

Publication date: 27 February 2018

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.090816.270317a

zbMATH Keywords

numerical examples error estimate semilocal convergence Newton-like method nonlinear operator equation Newton-Kantorovich theorem \(\gamma\)-condition

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15) Nonlinear ergodic theorems (47H25)

Cites Work

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Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space
A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition
On Halley-type iterations with free second derivative
On the convergence of a damped Newton-like method with modified right hand side vector
A third-order Newton-type method to solve systems of nonlinear equations
A family of fifth-order iterations composed of Newton and third-order methods
Kantorovich-type convergence criterion for inexact Newton methods
On Newton's method for solving equations containing Fréchet-differentiable operators of order at least two
Convergence on the iteration of Halley family in weak conditions
Modified Newton's method with third-order convergence and multiple roots
Some variant of Newton's method with third-order convergence.
Third-order methods from quadrature formulae for solving systems of nonlinear equations.
On the convergence of inexact two-point Newton-like methods on Banach spaces
Unified convergence domains of Newton-like methods for solving operator equations
On Newton-type methods with cubic convergence
On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
A modification of the classic conditions of Newton-Kantorovich for Newton's method
Third-order modification of Newton's method
Construction of third-order modifications of Newton's method
On the \(R\)-order of convergence of Newton's method under mild differentiability conditions
A semilocal convergence result for Newton's method under generalized conditions of Kantorovich
Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition
Newton's method under weak Kantorovich conditions
A variant of Newton's method with accelerated third-order convergence

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