scholarly journals Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search

1994 ◽  
Vol 19 (2) ◽  
pp. 352-389 ◽  
Author(s):  
Daniel Ralph
Keyword(s):  
Global Convergence ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonsmooth Equations ◽  
Path Search

scholarly journals The Newtonian Operator and Global Convergence Balls for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1074
Author(s):  
José A. Ezquerro ◽  
Miguel A. Hernández-Verón
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Convergence ◽  
Point Theorem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Integral Equation ◽  
The Fixed Point Theorem ◽  
Linear Integral

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

scholarly journals After notes on Chebyshev’s iterative method

2017 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. Amat ◽  
S. Busquier
Keyword(s):  
Global Convergence ◽  
Iterative Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Interpretation ◽  
Higher Order ◽  
Order Method ◽  
Chebyshev’S Method ◽  
Higher Order Method ◽  
Dynamical Properties

AbstractThis paper is a small review of Chebyshev’s method. The geometric interpretation as a generalization of Newton’s method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton’s method. Finally, some applications are revisited pointing out the advantages of Chebyshev’s method with respect Newton’s method.

scholarly journals How to Obtain Global Convergence Domains via Newton’s Method for Nonlinear Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 553 ◽  
Author(s):  
José Antonio Ezquerro ◽  
Miguel Ángel Hernández-Verón
Keyword(s):  
Global Convergence ◽  
Integral Equations ◽  
Newton’S Method ◽  
Existence And Uniqueness ◽  
Newton's Method ◽  
Uniqueness Of Solution ◽  
Nonlinear Integral Equations ◽  
Theoretical Significance

We use the theoretical significance of Newton’s method to draw conclusions about the existence and uniqueness of solution of a particular type of nonlinear integral equations of Fredholm. In addition, we obtain a domain of global convergence for Newton’s method.

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