Extended Newton-type method and its convergence analysis for nonsmooth generalized equations

2017 ◽  
Vol 19 (2) ◽  
pp. 1295-1313 ◽  
Author(s):  
M. H. Rashid
Keyword(s):  
Convergence Analysis ◽  
Generalized Equations ◽  
Type Method

scholarly journals Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 804
Author(s):  
Ioannis K. Argyros ◽  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Approximate Solution ◽  
Convergence Analysis ◽  
Banach Spaces ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Existence And Uniqueness ◽  
Numerical Illustration ◽  
Type Method ◽  
Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

Convergence Analysis of the Gauss–Newton-Type Method for Lipschitz-Like Mappings

2012 ◽  
Vol 158 (1) ◽  
pp. 216-233 ◽  
Author(s):  
M. H. Rashid ◽  
S. H. Yu ◽  
C. Li ◽  
S. Y. Wu
Keyword(s):  
Convergence Analysis ◽  
Type Method

scholarly journals Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Zhangsong Yao ◽  
Yan-Kuen Wu ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Variational Inclusions ◽  
Type Method ◽  
Common Solution ◽  
Mild Conditions

Iterative methods for solving variational inclusions and fixed-point problems have been considered and investigated by many scholars. In this paper, we use the Halpern-type method for finding a common solution of variational inclusions and fixed-point problems of pseudocontractive operators. We show that the proposed algorithm has strong convergence under some mild conditions.

scholarly journals Convergence analysis for a fast class of multi-step Chebyshev-Halley-type methods under weak conditions

2021 ◽  
Vol 4 (1) ◽  
pp. 34-43
Author(s):  
Samundra Regmi ◽  
◽  
Ioannis K. Argyros ◽  
Santhosh George ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Computational Cost ◽  
Convergence Domain ◽  
Convergence Region ◽  
Type Method ◽  
Precise Information ◽  
Numerical Examples ◽  
Lipschitz Constants ◽  
Theoretical Results

In this study a convergence analysis for a fast multi-step Chebyshe-Halley-type method for solving nonlinear equations involving Banach space valued operator is presented. We introduce a more precise convergence region containing the iterates leading to tighter Lipschitz constants and functions. This way advantages are obtained in both the local as well as the semi-local convergence case under the same computational cost such as: extended convergence domain, tighter error bounds on the distances involved and a more precise information on the location of the solution. The new technique can be used to extend the applicability of other iterative methods. The numerical examples further validate the theoretical results.

scholarly journals Convergence Properties of Extended Newton-type Iteration Method for Generalized Equations

2018 ◽  
Vol 10 (4) ◽  
pp. 1
Author(s):  
M. Khaton ◽  
M. Rashid ◽  
M. Hossain
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Iteration Method ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Convergence Properties ◽  
Closed Graph ◽  
Point Bar ◽  
Type Method ◽  
Set Valued Mapping

In this paper, we introduce and study the extended Newton-type method for solving generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\Omega\subseteq\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable in a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\Omega\subseteq \mathcal X\to \mathcal Y$ is linear and differentiable at a point $\bar{x}$, and $\mathcal F$ is a set-valued mapping with closed graph acting in Banach spaces $\mathcal X$ and $\mathcal Y$. Semilocal and local convergence of the extended Newton-type method are analyzed.

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