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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 ...
Expanding the aplicability of secant method with applications
(Bulletin of the Korean Mathematical Society, 2015-05)
We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center Lipschitz instead of just ...
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 ...
New semilocal and local convergence analysis for the Secant method
(Applied Mathematics and Computation, 2015-06)
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 ...
A new tool to study real dynamics: The convergence plane
(Applied Mathematics and Computation, 2014-12)
In this paper, the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way. This tool gives the information as ...
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 ...
Improving the Dynamics of Steffensen-type Methods
(Applied Mathematics and Information Sciences, 2015)
The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The
study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the ...
Extending the mesh independence for solving nonlinear equations using restricted domains
(International Journal of Applied and Computational Mathematics, 2017-12)
The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process ...
Inexact Newton Methods on Riemannian Manifolds
(Advances in iterative methods for nonlinear equations, 2016)
In this chapter we study of the Inexact Newton Method in order to solve problems on a Riemannian Manifold. We present standard notation and previous results on Riemannian manifolds. A local convergence study is presented ...
An Overview on Steffensen-Type Methods
(Advances in iterative methods for nonlinear equations, 2016)
In this chapter we present an extensive overview of Steffensen-type methods. We first present the real study of the methods and then we present the complex dynamics related this type of methods applied to different ...