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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 ...
Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains
(Journal of Mathematical Chemistry, 2017-08)
We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...
Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high
(Journal of Computational and Applied Mathematics, 2015-07)
We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...
Improved convergence analysis for Newton-like methods
(Numerical Algorithms, 2016-04)
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 ...
Extended convergence results for the Newton–Kantorovich iteration
(Journal of Computational and Applied Mathematics, 2015-10)
We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain ...
Third-degree anomalies of Traub's method
(Journal of Computational and Applied Mathematics, 2017-01)
Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...
Extending the applicability of the local and semilocal convergence of Newton's method
(Applied Mathematics and Computation, 2017-01)
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: ...
Enlarging the convergence domain of secant-like methods for equations
(Taiwanese Journal of Mathematics, 2015-04)
We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton's ...