Simultaneous roots for vectorial problems

Abstract

[EN] In this manuscript, we design an iterative step that can be added to any numerical process for solving systems of nonlinear equations. By means of this addition, the resulting iterative scheme obtains, simultaneously, all the solutions to the vectorial problem. Moreover, the order of this new iterative procedure duplicates that of their original partner. We apply this step to some known methods and analyse the behaviour of these new algorithms, obtaining simultaneously the roots of several nonlinear systems.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research was partially supported by Universitat Politècnica de València, Ayuda Movilidad Estancia Doctorado 01/10/2021 and Universitat Politècnica de València Contrato Predoctoral PAID-01-20-17 (UPV).Chinesta, F.; Cordero Barbero, A.; Garrido-Saez, N.; Torregrosa Sánchez, JR.; Triguero-Navarro, P. (2023). Simultaneous roots for vectorial problems. Computational and Applied Mathematics. 42(5). https://doi.org/10.1007/s40314-023-02366-y42