On the number of iterations of Newton's method for complex polynomials

2002 ◽  
Vol 22 (03) ◽  
Author(s):  
DIERK SCHLEICHER
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Complex Polynomials ◽  
Number Of Iterations

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

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 Distance to a Root of Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Somjate Chaiya
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Newton’S Method ◽  
Upper Bound ◽  
Newton's Method ◽  
Explicit Estimate ◽  
Roots Of Polynomials ◽  
Number Of Iterations

In 2002, Dierk Schleicher gave an explicit estimate of an upper bound for the number of iterations of Newton's method it takes to find all roots of polynomials with prescribed precision. In this paper, we provide a method to improve the upper bound given by D. Schleicher. We give here an iterative method for finding an upper bound for the distance between a fixed pointzin an immediate basin of a rootαtoα, which leads to a better upper bound for the number of iterations of Newton's method.

Efficiency of Solution Methods for Kepler’s Equation

2016 ◽  
Vol 851 ◽  
pp. 587-592
Author(s):  
João Francisco Nunes de Oliveira ◽  
Roberta Veloso Garcia ◽  
Hélio Koiti Kuga ◽  
Estaner Claro Romão
Keyword(s):  
Iterative Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Kepler's Equation ◽  
Eccentric Orbits ◽  
Kepler’S Equation ◽  
Solution Methods ◽  
Number Of Iterations

This article discusses, in the case of eccentric orbits, some solution methods for Kepler's equation, for instance: Newton's method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each method needs to lead to a solution within the specified tolerance. The solution using Fourier-Bessel series is not an iterative method, however, it was analyzed the number of terms required to achieve the accuracy of the prescribed solution.

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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