How to improve the domain of parameters for Newton’s method

2015 ◽  
Vol 48 ◽  
pp. 91-101 ◽  
Author(s):  
J.A. Ezquerro ◽  
M.A. Hernández-Verón
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Domain Of Parameters

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.

scholarly journals Improving the domain of parameters for Newton’s method with applications

2017 ◽  
Vol 318 ◽  
pp. 124-135 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Ángel Alberto Magreñán ◽  
Juan Antonio Sicilia
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Domain Of Parameters

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations
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