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Study of local convergence and dynamics of a king-like two-step method with applications
(Mathematics, 2020-07-01)
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...
Weaker conditions for inexact mutitpoint Newton-like methods
(Journal of Mathematical Chemistry, 2020-01)
In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability. We will ...
Advances in the Semilocal Convergence of Newton's Method with Real-World Applications
(Mathematics, 2019-03-24)
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 ...
Extending the Applicability of Stirling's Method
(Mathematics, 2020-01)
Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require ...
Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
(Journal of Mathematical Chemistry, 2016-08)
We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...
Improving the domain of parameters for Newton's method with applications
(Journal of Computational and Applied Mathematics, 2017-07)
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 ...
Local Convergence and the Dynamics of a Two-Step Newton-Like Method
(International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2016-05)
We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.
On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence
(Journal of Computational and Applied Mathematics, 2016-05)
We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence ...
Local convergence of a relaxed two-step Newton like method with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
New improved convergence analysis for Newton-like methods with applications
(Journal of Mathematical Chemistry, 2017-08)
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 ...