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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 ...
Starting points for Newton’s method under a center Lipschitz condition for the second derivative
(Journal of Computational and Applied Mathematics, 2018-03)
We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...
A study of 16 years old student learning strategies from a neuropsychological perspective: An intervention proposal
(Trends in Neuroscience and Education, 2018-06)
Scientific achievements related to brain processes provide innovation and improvements in students' learning. The aim of this study was to analyse, relate, and compare learning strategies and academic performance of students ...
The hologram as a teaching medium for the acquisition of STEM contents
(International Journal of Learning Technology, 2018)
The aim of the work presented in this article is to assess whether the use of a hologram enhances the meaningful learning of cellular division contents. A pilot phase has been carried out with a sample of students of 4th ...
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 ...
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 ...
Measures of the Basins of Attracting n-Cycles for the Relaxed Newton's Method
(Advances in iterative methods for nonlinear equations, 2016)
The relaxed Newton's method modifies the classical Newton's method with a parameter h in such a way that when it is applied to a polynomial with multiple roots and we take as parameter one of these multiplicities, it is ...
On the behavior of chebyshev's method applied to cubic polynomials
(Civil-Comp Proceedings, 2014)
This paper shows the dynamical behavior of the well-known Chebyshev method when it is applied to cubic polynomials. We present the scaling theorem associated to the method and we study the real dynamics of the method. The ...