Alicia Cordero

TL;DR: In this article, the authors construct several families of iterative methods with memory from one without memory, that is, they have increased the order of convergence without adding new functional evaluations, which yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members.

TL;DR: This work provides a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009) that satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory.

TL;DR: This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P, Generalitat Valenciana PROMETEO/2016/089 and Schlumberger Foundation-Faculty for Future Program.

TL;DR: In this article, a parametric family including Newton's and Traub's iterative schemes is presented and its local convergence and dynamical behavior on quadratic polynomials are studied.

TL;DR: This chapter presents an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc.