inexact newton methods
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scholarly journals Ball convergence theorem for inexact Newton methods in Banach space

2020 ◽  
Vol 29 (2) ◽  
pp. 113-120
Author(s):  
IOANNIS K. ARGYROS ◽  
GEORGE SANTHOSH
Keyword(s):  
Banach Space ◽  
Nonlinear Equation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Newton Methods ◽  
Convergence Conditions ◽  
Inexact Newton Methods ◽  
Numerical Examples ◽  
Ball Convergence ◽  
Local Convergence Analysis

We present a local convergence analysis for inexact Newton methods in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Frèchet-derivative of the operator involved. Numerical examples are also provided in this study.

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