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Extending the applicability of the local and semilocal convergence of Newton's method
We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: ...
Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields
The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...
Improved semilocal convergence analysis in Banach space with applications to chemistry
We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds ...
Improved convergence analysis for Newton-like methods
We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in ...
Advances in the Semilocal Convergence of Newton's Method with Real-World Applications
The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...
On the convergence of an optimal fourth-order family of methods and its dynamics
In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...
A unified convergence analysis for secant-type methods
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...
Extending the convergence domain of Newton's method for twice Frechet differentiable operators
We present a semi-local convergence analysis of Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using center-Lipschitz condition on the first and the ...
Improving the domain of parameters for Newton's method with applications
We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...
New improved convergence analysis for Newton-like methods with applications
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...