scholarly journals Newton’s method on the complex exponential function

1999 ◽  
Vol 351 (6) ◽  
pp. 2499-2513 ◽  
Author(s):  
Mako E. Haruta
Keyword(s):  
Exponential Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Complex Exponential

Julia sets of Newton’s method for a class of complex-exponential function F(z)=P(z)e Q(z)

2010 ◽  
Vol 62 (4) ◽  
pp. 955-966 ◽  
Author(s):  
Xing-Yuan Wang ◽  
Yi-Ke Li ◽  
Yuan-Yuan Sun ◽  
Jun-Mei Song ◽  
Feng-Dan Ge
Keyword(s):  
Exponential Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Julia Sets ◽  
Complex Exponential

Algorithms for Solving the Catch Equation Forward and Backward in Time

1982 ◽  
Vol 39 (1) ◽  
pp. 197-202 ◽  
Author(s):  
S. E. Sims
Keyword(s):  
Mortality Rate ◽  
Numerical Solution ◽  
Exponential Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Padé Approximation ◽  
Approximate Solutions ◽  
Fishing Mortality ◽  
Convergence Criteria ◽  
Pade Approximation

Approximate solutions to the catch equation for the fishing mortality rate both forward and backward in time are obtained with an application of the diagonal Padé approximation of degree four to the exponential function. In either case the resulting approximation as well as Pope's estimate are shown to serve quite well as starting values for Newton's Method which is used to obtain a numerical solution of the catch equation. Convergence criteria for Newton's Method are discussed in each setting.Key words: catch equation, Newton's method, Padé approximation, Pope's estimate

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

scholarly journals On the speed of convergence of Newton’s method for complex polynomials

2015 ◽  
Vol 85 (298) ◽  
pp. 693-705 ◽  
Author(s):  
Todor Bilarev ◽  
Magnus Aspenberg ◽  
Dierk Schleicher
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Speed Of Convergence ◽  
Complex Polynomials
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