Vázquez-Lozano, JE.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2018). Dynamical analysis on cubic polynomials of Damped Traub s method for approximating multiple roots. Applied Mathematics and Computation. 328:82-99. https://doi.org/10.1016/j.amc.2018.01.043
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/120344
Title:
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Dynamical analysis on cubic polynomials of Damped Traub s method for approximating multiple roots
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Author:
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Vázquez-Lozano, Juan Enrique
Cordero Barbero, Alicia
Torregrosa Sánchez, Juan Ramón
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UPV Unit:
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Universitat Politècnica de València. Instituto Universitario de Tecnología Nanofotónica - Institut Universitari de Tecnologia Nanofotònica
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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[EN] In this paper, the performance of a parametric family including Newton¿s and Traub¿s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well ...[+]
[EN] In this paper, the performance of a parametric family including Newton¿s and Traub¿s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots. The fixed and critical points, and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work. From the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots, and also other ones with very unstable behavior.
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Subjects:
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Nonlinear equations
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Iterative methods
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Multiple roots
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Complex dynamics
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Convergence regions
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Copyrigths:
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Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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Source:
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Applied Mathematics and Computation. (issn:
0096-3003
)
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DOI:
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10.1016/j.amc.2018.01.043
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Publisher:
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Elsevier
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Publisher version:
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http://doi.org/10.1016/j.amc.2018.01.043
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Project ID:
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info:eu-repo/grantAgreement/MINECO//MTM2014-52016-C2-2-P/ES/DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES./
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/
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Thanks:
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This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P Spain and Generalitat Valenciana PROMETEO/2016/089 Spain
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Type:
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Artículo
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