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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 ...
Improved local convergence analysis of the Gauss-Newton method under a majorant condition
(Computational Optimization and Applications, 2015-03)
We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, 2008), ...
New improved convergence analysis for the secant method
(Mathematics and Computers in Simulation, 2016-01)
We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz ...
On the convergence of an optimal fourth-order family of methods and its dynamics
(Applied Mathematics and Computation, 2015-02)
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 ...