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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

In this chapter we will study the convex composite optimizations problem.

Capítulo del libro "Iterative Methods and Their Dynamics with Applications"

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 ...