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 ...

In this paper, the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way. This tool gives the information as ...

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 ...

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 ...

We present a local convergence analysis of the proximal Gauss-Newton method for solving penalized nonlinear least squares problems in a Hilbert space setting. Using more precise majorant conditions than in earlier studies ...

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information ...

The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the -iterative methods and the well-known Chebyshev-Halley family. We find the ...

We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...

The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used ...