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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 ...
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 ...
Ball convergence of a sixth-order Newton-like method based on means under weak conditions
(Journal of Mathematical Chemistry, 2018-08)
We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...
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 ...
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 ...
A contemporary study of iterative methods: Convergence, dynamics and applications
(Elsevier, 2018)
A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...