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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 ...
Herramienta pedagógica basada en el desarrollo de una aplicación informática para la mejora del aprendizaje en matemática avanzada
(Revista Española de Pedagogía, 2019-09-01)
El estudio dinámico de los métodos iterativos ha aumentado en las últimas décadas debido al desarrollo de los ordenadores, aspecto por el cual se ha visto la necesidad de incluir la enseñanza de estos métodos en los planes ...
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, ...
Complexity of an Homotopy Method at the Neighbourhood of a Zero
(Advances in iterative methods for nonlinear equations, 2016)
This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered ...
Extending the Applicability of Stirling's Method
(Mathematics, 2020-01)
Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require ...
Secant-like methods
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we study the problem of finding a locally unique solution x of equation F(x) = 0, (13.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space χ with values in a Banach ...
Gauss-newton method with applications to convex optimization
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we will study the convex composite optimizations problem.
Preface
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Capítulo del libro "Iterative Methods and Their Dynamics with Applications"
Extending the kantorovich theory for solving equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Let X, Y be Banach spaces, D ⊂ X be convex, F : D ⊂ X → Y be a Fréchet differentiable operator. We shall determine a solution x of the equation F(x) = 0, Many problems from Applied Sciences can be solved finding the solutions ...