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King-werner-like methods free of derivatives
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Recently, Argyros and Ren in [6] studied King-Werner-like methods for approximating a locally unique solution x of equation (formula presented).
Iterative methods and their dynamics with applications: A contemporary study
(CRC Press, 2017)
Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced ...
Sixth-order iterative methods
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
We develop sixth-order iterative methods in order to approximate zeros x of the function f defined on the real line. This method can be used to solve many 64problems from computational sciences and other disciplines ...
King-Werner-type methods of order 1 + √2
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-differentiable operator defined on a convex subset D of a Banach space X with ...
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 ...
A new fourth-order family for solving nonlinear problems and its dynamics
(Journal of Mathematical Chemistry, 2015-03)
In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
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 ...
A first overview on the real dynamics of Chebyshev's method
(Journal of Computational and Applied Mathematics, 2017-07)
In this paper we explore some properties of the well known root-finding Chebyshev’s method applied to polynomials defined on the real field. In particular we are interested in showing the existence of extraneous fixed ...