scholarly journals Accelerated convergence in Newton's method for approximating square roots

2005 ◽  
Vol 177 (1) ◽  
pp. 225-229 ◽  
Author(s):  
M.A. Hernández ◽  
N. Romero
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Square Roots ◽  
Accelerated Convergence

Accelerated Convergence in Newton’s Method

SIAM Review ◽  
1996 ◽  
Vol 38 (4) ◽  
pp. 658-659 ◽  
Author(s):  
William F. Ford ◽  
James A. Pennline
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Accelerated Convergence

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

Accelerated Convergence in Newton’s Method

SIAM Review ◽  
1994 ◽  
Vol 36 (2) ◽  
pp. 272-276 ◽  
Author(s):  
Jürgen Gerlach
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Accelerated Convergence

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.

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