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A study of dynamics via Mobius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions
(Journal of Computational and Applied Mathematics, 2018-12-15)
A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight ...
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 ...
New Improvement of the Domain of Parameters for Newton’s Method
(Mathematics, 2020-01)
There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability ...
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 ...
Study of local convergence and dynamics of a king-like two-step method with applications
(Mathematics, 2020-07-01)
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...
Weaker conditions for inexact mutitpoint Newton-like methods
(Journal of Mathematical Chemistry, 2020-01)
In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability. We will ...
Advances in the Semilocal Convergence of Newton's Method with Real-World Applications
(Mathematics, 2019-03-24)
The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...
The Kumon Method: Its Importance in the Improvement on the Teaching and Learning of Mathematics from the First Levels of Early Childhood and Primary Education
(Mathematics, 2019-01)
The present work gathers an educational experience based on the application of the personalized Kumon Mathematics Method, carried out in the school year 2015-2016, in which 30,849 students and 230 teachers from several ...
Study of a high order family: Local convergence and dynamics
(Mathematics, 2019-03-01)
The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
