An iterative scheme to obtain multiple solutions simultaneously

[EN] In this manuscript, we propose an iterative step that, combined with any other method, allows us to obtain an iterative scheme for approximating the simple roots of a polynomial simultaneously. We show that adding this step, the order of convergence of the new scheme is tripled respect to the o...

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Detalles Bibliográficos
Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Garrido-Saez, Neus|||0000-0002-7903-8591, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Triguero-Navarro, Paula|||0000-0002-7319-9992
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/203329
Acceso en línea:https://riunet.upv.es/handle/10251/203329
Access Level:acceso abierto
Palabra clave:Nonlinear equations
Iterative methods
Simultaneous solutions
Multiple roots
Simultaneous multiple roots
MATEMATICA APLICADA
Descripción
Sumario:[EN] In this manuscript, we propose an iterative step that, combined with any other method, allows us to obtain an iterative scheme for approximating the simple roots of a polynomial simultaneously. We show that adding this step, the order of convergence of the new scheme is tripled respect to the original one. With this idea, we also present an iterative method that obtains multiple solutions of any nonlinear equation simultaneously, without the need to know the multiplicity of the solutions. We conclude with several numerical experiments to confirm the behaviour of the proposed methods.& COPY; 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).