From Square Roots to n-th Roots: Newton's Method in Disguise

1999 ◽  
Vol 30 (5) ◽  
pp. 387
Author(s):  
W. M. Priestley
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Square Roots

Newton's Method for Square Root: A Spreadsheet Investigation and Extension into Chaos

1998 ◽  
Vol 91 (7) ◽  
pp. 576-585
Author(s):  
Sharon Dugdale
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Square Root ◽  
Square Roots ◽  
Mathematical Ideas ◽  
Spreadsheet Model

Spreadsheets have become popular and effective tools for the dynamic exploration of recursively defined functions, the generalization of solutions to problems, and the visualization of mathematical ideas. This article discusses a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos

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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