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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 ...
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: ...
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 ...
Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions
(Numerical Algorithms, 2017-02)
We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...
On the convergence of inexact two-point Newton-like methods on Banach spaces
(Applied Mathematics and Computation, 2015-08)
We present a unified convergence analysis of Inexact Newton like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The ...
On the convergence of a damped Newton-like method with modified right hand side vector
(Applied Mathematics and Computation, 2015-09)
We present a convergence analysis for a damped Newton like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special ...