Cordero Barbero, A.; Soleymani, F.; Torregrosa Sánchez, JR. (2014). Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?. Applied Mathematics and Computation. 244:398-412. https://doi.org/10.1016/j.amc.2014.07.010
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/54856
Title:
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Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?
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Author:
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Cordero Barbero, Alicia
Soleymani, Fazlollah
Torregrosa Sánchez, Juan Ramón
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UPV Unit:
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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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This paper deals with the real dynamical analysis of iterative methods for solving nonlinear systems on vectorial quadratic polynomials. We use the extended concept of critical point and propose an easy test to determine ...[+]
This paper deals with the real dynamical analysis of iterative methods for solving nonlinear systems on vectorial quadratic polynomials. We use the extended concept of critical point and propose an easy test to determine the stability of fixed points to multivariate rational functions. Moreover, an Scaling Theorem for different known methods is satisfied. We use these tools to analyze the dynamics of the operator associated to known iterative methods on vectorial quadratic polynomials of two variables. The dynamical behavior of Newton's method is very similar to the obtained in the scalar case, but this is not the case for other schemes. Some procedures of different orders of convergence have been analyzed under this point of view and some "dangerous" numerical behavior have been found, as attracting strange fixed points or periodic orbits. 2014 Elsevier Inc. All rights reserved.
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Subjects:
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Nonlinear system of equations
,
Iterative method
,
Basin of attraction
,
Dynamical plane
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Stability
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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.2014.07.010
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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.2014.07.010
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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//SP20120474/
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Thanks:
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This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and Universitat Politecnica de Valencia SP20120474.
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Type:
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Artículo
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