Convergence of Newton's Method and Uniqueness of the Solution of Equations in Banach Spaces II

2003 ◽  
Vol 19 (2) ◽  
pp. 405-412 ◽  
Author(s):  
Xing Hua Wang ◽  
Chong Li
Keyword(s):  
Banach Spaces ◽  
Newton’S Method ◽  
Newton's Method ◽  
Solution Of Equations ◽  
Uniqueness Of The Solution

scholarly journals Unified Local Convergence for Newton’s Method and Uniqueness of the Solution of Equations under Generalized Conditions in a Banach Space

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 463 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Ángel Alberto Magreñán ◽  
Lara Orcos ◽  
Íñigo Sarría
Keyword(s):  
Banach Space ◽  
Newton’S Method ◽  
Newton's Method ◽  
Convergence Region ◽  
Precise Information ◽  
Solution Of Equations ◽  
Lipschitz Constants ◽  
Uniqueness Of The Solution ◽  
Generalized Newton ◽  
Theoretical Results

Under the hypotheses that a function and its Fréchet derivative satisfy some generalized Newton–Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton’s method, and of the uniqueness ball for the solution of the equations, are given for Banach space-valued operators. Some of the existing results are improved with the advantages of larger convergence region, tighter error estimates on the distances involved, and at-least-as-precise information on the location of the solution. These advantages are obtained using the same functions and Lipschitz constants as in earlier studies. Numerical examples are used to test the theoretical 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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