A multistep Steffensen-type method for solving nonlinear systems of equations

[EN] This paper is devoted to the semilocal analysis of a high-order Steffensen-type method with frozen divided differences. The methods are free of bilinear operators and derivatives, which constitutes the main limitation of the classical high-order iterative schemes. Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions than the classical Steffensen method.This work was supported supported in part by by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 19374/PI/14, by the project of Generalitat Valenciana Prometeo/2016/089 and the projects MTM2015-64382-P (MINECO/FEDER), MTM2014-52016-C2-1-P and MTM2014-52016-C2-2-P of the Spanish Ministry of Science and InnovationAmat, S.; Argyros, IK.; Busquier, S.; Hernández-Verón, MA.; Magreñán, AA.; Martínez Molada, E. (2020). A multistep Steffensen-type method for solving nonlinear systems of equations. Mathematical Methods in the Applied Sciences. 43(13):7518-7536. https://doi.org/10.1002/mma.559975187536431