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Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in banach spaces
(Journal of the Korean Mathematical Society, 2015-01)
We present a semilocal convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica. and Neta. These ...
A unified convergence analysis for secant-type methods
(Journal of the Korean Mathematical Society, 2014-11)
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...
Relaxed secant-type methods
(Nonlinear Studies, 2014-06)
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation ...
Extending the domain of starting points for Newton's method under conditions on the second derivative
(Journal of Computational and Applied Mathematics, 2018-10)
In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...
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 ...
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 ...
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 ...
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 ...
Expanding the applicability of the Secant method under weaker conditions
(Applied Mathematics and Computation, 2015-09)
We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on ...