scholarly journals Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

2018 ◽  
Vol 56 (1) ◽  
pp. 23-34
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Newton Method ◽  
Fourth Order ◽  
Local Convergence ◽  
Systems Of Nonlinear Equations ◽  
Order Method ◽  
First Derivative ◽  
Fourth Order Method ◽  
Order Four ◽  
Local Convergence Analysis

Abstract Local convergence analysis of a fourth order method considered by Sharma et. al in [19] for solving systems of nonlinear equations. Using conditions on derivatives upto the order five, they proved that the method is of order four. In this study using conditions only on the first derivative, we prove the convergence of the method in [19]. This way we extended the applicability of the method. Numerical example which do not satisfy earlier conditions but satisfy our conditions are presented in this study.

scholarly journals On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Fangqin Zhou
Keyword(s):  
Convergence Analysis ◽  
Newton Method ◽  
Local Convergence ◽  
Singular Systems ◽  
Inexact Newton Method ◽  
Systems Of Equations ◽  
Convergence Ball ◽  
Special Cases ◽  
Majorant Condition ◽  
Local Convergence Analysis

We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases.

scholarly journals Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions

2016 ◽  
Vol 54 (2) ◽  
pp. 37-46
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Local Convergence ◽  
Convergence Order ◽  
Order Method ◽  
Numerical Examples ◽  
Local Convergence Analysis

Abstract In the present paper, we study the local convergence analysis of a fifth convergence order method considered by Sharma and Guha in [15] to solve equations in Banach space. Using our idea of restricted convergence domains we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

scholarly journals Local convergence for a family of sixth order methods with parameters

2021 ◽  
Vol 5 (1) ◽  
pp. 300-305
Author(s):  
Christopher I. Argyros ◽  
◽  
Michael Argyros ◽  
Ioannis K. Argyros ◽  
Santhosh George ◽  
...  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Real Line ◽  
Local Convergence ◽  
Sixth Order ◽  
Numerical Examples ◽  
The Real ◽  
First Derivative ◽  
Local Convergence Analysis ◽  
Methods Numerical

Local convergence of a family of sixth order methods for solving Banach space valued equations is considered in this article. The local convergence analysis is provided using only the first derivative in contrast to earlier works on the real line using the seventh derivative. This way the applicability is expanded for these methods. Numerical examples complete the article.

High Convergence Order Q-Step Methods for Solving Equations and Systems of Equations

2020 ◽  
pp. 102-109
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Iterative Methods ◽  
Error Bounds ◽  
Local Convergence ◽  
Not Given ◽  
Systems Of Equations ◽  
Numerical Examples ◽  
First Derivative ◽  
Solving Equations ◽  
Local Convergence Analysis

The local convergence analysis of iterative methods is important since it demonstrates the degree of diffculty for choosing initial points. In the present study, we introduce generalized multi-step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative which actually appears in the methods in contrast to earlier works using hypotheses on higher order derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions not given in earlier studies. Numerical examples conclude this study.

Sign in / Sign up

Export Citation Format

Share Document