Chicharro López, FI.; Cordero Barbero, A.; Gutiérrez, JM.; Torregrosa Sánchez, JR. (2013). Complex dynamics of derivative-free methods for nonlinear equations. Applied Mathematics and Computation. 219(12):7023-7035. https://doi.org/10.1016/j.amc.2012.12.075
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/54854
Title:
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Complex dynamics of derivative-free methods for nonlinear equations
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Author:
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Chicharro López, Francisco Israel
Cordero Barbero, Alicia
Gutiérrez, José M.
Torregrosa Sánchez, Juan Ramón
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UPV Unit:
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Universitat Politècnica de València. Instituto Universitario de Telecomunicación y Aplicaciones Multimedia - Institut Universitari de Telecomunicacions i Aplicacions Multimèdia
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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The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. ...[+]
The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. Different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients. The property of immersion of the basins of attraction in all cases is analyzed. 2013 Elsevier Inc. All rights reserved.
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Subjects:
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Nonlinear equation
,
Iterative method
,
Derivative-free method
,
Complex dynamics
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Parameters plane
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Fixed point
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Critical point
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Immersed basin of attraction
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Copyrigths:
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Cerrado |
Source:
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Applied Mathematics and Computation. (issn:
0096-3003
) (eissn:
1873-5649
)
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DOI:
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10.1016/j.amc.2012.12.075
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.amc.2012.12.075
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Project ID:
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info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
info:eu-repo/grantAgreement/UPV//PAID-06-10-2285/
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Thanks:
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This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.
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Type:
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Artículo
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