Alicia Cordero

TL;DR: This paper presents a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence, and finds that these proposed methods are very useful in high precision computations.

TL;DR: A dynamical study of the Ostrowski–Chun family of iterative methods on quadratic polynomials will use dynamical tools such as the analysis of fixed and critical points, and the calculation of parameter planes, to find the most stable members of the family.

TL;DR: The stability of the Traub's method is analyzed on cubic polynomials, showing the existence of very small regions with unstable behavior and the performance of the method on cubic matrix equations arising in control theory is presented, showing a good performance.

TL;DR: In this paper, the authors proposed a new fourth-order optimal scheme for obtaining the multiple roots of nonlinear equations. But, they gave the flexibility in their proposed schemes only at the second step (not at the first step) in order to explore new schemes.

TL;DR: A survey on the existing techniques used to design optimal iterative schemes for solving nonlinear equations is presented, focusing on such procedures that use some evaluations of the derivative of the nonlinear function.