Local convergence of parameter based method with six and eighth order of convergence

2020 ◽  
Vol 58 (4) ◽  
pp. 841-853
Author(s):  
Ali Saleh Alshomrani ◽  
Ramandeep Behl ◽  
P. Maroju
Keyword(s):  
Local Convergence ◽  
Order Of Convergence ◽  
Eighth Order

scholarly journals Extended local convergence for Newton-type solver under weak conditions

2021 ◽  
Vol 66 (4) ◽  
pp. 757-768
Author(s):  
Ioannis K. Argyros ◽  
◽  
Santhosh George ◽  
Kedarnath Senapati ◽  
◽  
...  
Keyword(s):  
Local Convergence ◽  
Order Of Convergence ◽  
Basins Of Attraction ◽  
Dimensional Euclidean Space ◽  
Test Problems ◽  
Eighth Order ◽  
Convergence Conditions ◽  
Numerical Examples ◽  
Special Case ◽  
Methods Numerical

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence was shown earlier in the special case of the k-dimensional Euclidean space, using hypotheses up to the eighth derivative although these derivatives do not appear in the method. We show convergence using only the rst derivative. This way we extend the applicability of the methods. Numerical examples are used to show the convergence conditions. Finally, the basins of attraction of the method, on some test problems are presented.

scholarly journals Local Convergence Analysis of an Eighth Order Scheme Using Hypothesis Only on the First Derivative

Algorithms ◽  
2016 ◽  
Vol 9 (4) ◽  
pp. 65 ◽  
Author(s):  
Ioannis Argyros ◽  
Ramandeep Behl ◽  
Sandile Motsa
Keyword(s):  
Convergence Analysis ◽  
Local Convergence ◽  
Eighth Order ◽  
First Derivative ◽  
Order Scheme ◽  
Local Convergence Analysis

scholarly journals On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Efficiency Index ◽  
Order Convergence ◽  
Eighth Order ◽  
Additional Function ◽  
Numerical Comparisons ◽  
With Memory

Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods.

scholarly journals Local Convergence of an Optimal Eighth Order Method under Weak Conditions

Algorithms ◽  
2015 ◽  
Vol 8 (3) ◽  
pp. 645-655 ◽  
Author(s):  
Ioannis Argyros ◽  
Ramandeep Behl ◽  
S.S. Motsa
Keyword(s):  
Local Convergence ◽  
Order Method ◽  
Eighth Order

On improved Steffensen type methods with optimal eighth-order of convergence

2015 ◽  
Vol 6 (1) ◽  
pp. 223
Author(s):  
Munish Kansal ◽  
V. Kanwar ◽  
Saurabh Bhatia
Keyword(s):  
Order Of Convergence ◽  
Eighth Order

scholarly journals Optimal Steffensen-type methods with eighth order of convergence

2011 ◽  
Vol 62 (12) ◽  
pp. 4619-4626 ◽  
Author(s):  
F. Soleymani ◽  
S. Karimi Vanani
Keyword(s):  
Order Of Convergence ◽  
Eighth Order

scholarly journals A family of modified Ostrowski’s methods with optimal eighth order of convergence

2011 ◽  
Vol 24 (12) ◽  
pp. 2082-2086 ◽  
Author(s):  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Order Of Convergence ◽  
Eighth Order

An Optimal Reconstruction of Chebyshev–Halley-Type Methods with Local Convergence Analysis

2019 ◽  
Vol 17 (05) ◽  
pp. 1940017
Author(s):  
Ali Saleh Alshomrani ◽  
Ioannis K. Argyros ◽  
Ramandeep Behl
Keyword(s):  
Local Convergence ◽  
Real Life ◽  
Eighth Order ◽  
Dynamical Study ◽  
First Order ◽  
Life Problems ◽  
Local Convergence Analysis ◽  
Lipschitz Conditions ◽  
Scalar Equations ◽  
Basins Of Attractions

Our principle aim in this paper is to present a new reconstruction of classical Chebyshev–Halley schemes having optimal fourth and eighth-order of convergence for all parameters [Formula: see text] unlike in the earlier studies. In addition, we analyze the local convergence of them by using hypotheses requiring the first-order derivative of the involved function [Formula: see text] and the Lipschitz conditions. In addition, we also formulate their theoretical radius of convergence. Several numerical examples originated from real life problems demonstrate that they are applicable to a broad range of scalar equations, where previous studies cannot be used. Finally, a dynamical study of them also demonstrates that bigger and more promising basins of attractions are obtained.

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