Alicia Cordero

TL;DR: The performance of a parametric family including Newton's and Traub's schemes on multiple roots is analyzed and members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots are identified.

TL;DR: In this article, a family of multi-point iterative methods for solving systems of nonlinear equations is described, and convergence order is proved to be 2d + 1, where d is the order of the partial derivatives required to be zero in the solution.

TL;DR: An efficient sixth-order scheme for solving nonlinear systems of equations, with only two steps in its iterative expression, which belongs to a new parametric class of methods whose order of convergence is, at least, four.

TL;DR: A class of iterative schemes appears, for which those elements able to converge with very far initial estimations are analyzed, which generalizes many known iterative methods which are obtained for particular values of the parameters.

TL;DR: In this article , a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations is proposed.