Ball Convergence of a Sixth Order Iterative Method

2015 ◽  
pp. 297-307
Author(s):  
George A. Anastassiou ◽  
Ioannis K. Argyros
Keyword(s):  
Iterative Method ◽  
Sixth Order ◽  
Ball Convergence

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.

A modified Chebyshev’s iterative method with at least sixth order of convergence

2008 ◽  
Vol 206 (1) ◽  
pp. 164-174 ◽  
Author(s):  
S. Amat ◽  
M.A. Hernández ◽  
N. Romero
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Sixth Order

Ball convergence of a sixth-order Newton-like method based on means under weak conditions

2018 ◽  
Vol 56 (7) ◽  
pp. 2117-2131 ◽  
Author(s):  
Á. A. Magreñán ◽  
I. K. Argyros ◽  
J. J. Rainer ◽  
J. A. Sicilia
Keyword(s):  
Sixth Order ◽  
Ball Convergence

Semilocal convergence of a sixth order iterative method for quadratic equations

2012 ◽  
Vol 62 (7) ◽  
pp. 833-841 ◽  
Author(s):  
S. Amat ◽  
M.A. Hernández ◽  
N. Romero
Keyword(s):  
Iterative Method ◽  
Semilocal Convergence ◽  
Sixth Order ◽  
Quadratic Equations

scholarly journals Ball convergence for a fourth order iterative method

2018 ◽  
Vol 1139 ◽  
pp. 012035
Author(s):  
Ioannis K Argyros ◽  
Ramandeep Behl
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Ball Convergence

scholarly journals Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 260 ◽  
Author(s):  
Janak Sharma ◽  
Ioannis Argyros ◽  
Sunil Kumar
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Higher Order ◽  
High Order ◽  
Convergence Order ◽  
Eighth Order ◽  
First Derivative ◽  
Ball Convergence ◽  
Derivatives Of

The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since their convergence is not guaranteed. The convergence in this paper is shown, relying only on the first derivative. That is how we expand the applicability of some popular methods.

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