scholarly journals Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative

1999 ◽  
Vol 26 (4) ◽  
pp. 457-465
Author(s):  
Ioannis Argyros
Keyword(s):  
Local Convergence ◽  
Fréchet Derivative ◽  
Affine Invariant ◽  
Newton Methods ◽  
Inexact Newton Methods ◽  
Frechet Derivative

Local convergence of deformed Euler–Halley-type methods in Banach space under weak conditions

2017 ◽  
Vol 10 (02) ◽  
pp. 1750086
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Nonlinear Equation ◽  
Convergence Analysis ◽  
Error Estimates ◽  
Local Convergence ◽  
Fréchet Derivative ◽  
Convergence Ball ◽  
Numerical Examples ◽  
Frechet Derivative ◽  
Local Convergence Analysis

We present a unified local convergence analysis for deformed Euler–Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The convergence ball and error estimates are given for these methods under hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the second Fréchet derivative. Numerical examples are also provided in this study.

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