How to find all roots of complex polynomials by Newton’s method

2001 ◽  
Vol 146 (1) ◽  
pp. 1-33 ◽  
Author(s):  
John Hubbard ◽  
Dierk Schleicher ◽  
Scott Sutherland
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Complex Polynomials

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

Newton’s Method for Complex Polynomials: Cayley’s Problem

1986 ◽  
pp. 93-102
Author(s):  
Heinz-Otto Peitgen ◽  
Peter H. Richter
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Complex Polynomials

scholarly journals A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton’s method

2012 ◽  
Vol 82 (281) ◽  
pp. 443-457 ◽  
Author(s):  
Béla Bollobás ◽  
Malte Lackmann ◽  
Dierk Schleicher
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Complex Polynomials

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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