scholarly journals Inexact Newton’s method for generalized operator equations in Banach spaces

2018 ◽  
Vol 17 (4) ◽  
pp. 85-97
Author(s):  
Vipin Kumar Singh
Keyword(s):  
Banach Spaces ◽  
Newton’S Method ◽  
Newton's Method ◽  
Operator Equations ◽  
Generalized Operator

scholarly journals New Improvement of the Domain of Parameters for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 103 ◽  
Author(s):  
Cristina Amorós ◽  
Ioannis K. Argyros ◽  
Daniel González ◽  
Ángel Alberto Magreñán ◽  
Samundra Regmi ◽  
...  
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Convergence Domain ◽  
Operator Equations ◽  
Numerical Examples ◽  
New Information ◽  
Analogous Manner ◽  
The One ◽  
Domain Of Parameters ◽  
Local Convergence Analysis

There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability of the methods. The new idea involves the construction of a tighter set than the ones used before also containing the iterates leading to at least as tight Lipschitz parameters and consequently a finer local as well as a semi-local convergence analysis. We used Newton’s method to demonstrate our technique. However, our technique can be used to extend the applicability of other methods too in an analogous manner. In particular, the new information related to the location of the solution improves the one in previous studies. This work also includes numerical examples that validate the proven results.

Mild Differentiability Conditions for Newton's Method in Banach Spaces

2020 ◽  
Author(s):  
José Antonio Ezquerro Fernandez ◽  
Miguel Ángel Hernández Verón
Keyword(s):  
Banach Spaces ◽  
Newton’S Method ◽  
Newton's Method
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