A multidimensional dynamical approach to iterative methods with memory
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Otros documentos de la autoría: Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura
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A multidimensional dynamical approach to iterative methods with memoryFecha de publicación
2015-11-15Editor
ElsevierCita bibliográfica
CAMPOS SANCHO, Beatriz; CORDERO BARBERO, Alicia; TORREGROSA, Juan R.; VINDEL CAÑAS, María Purificación. A multidimensional dynamical approach to iterative methods with memory. Applied Mathematics and Computation (2015), v. 271, pp. 701–715Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0096300315012941Versión
info:eu-repo/semantics/sumittedVersionPalabras clave / Materias
Resumen
A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made. We have designed new methods with memory from Steffensen’ or Traub’s schemes, as well as from a parametric ... [+]
A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made. We have designed new methods with memory from Steffensen’ or Traub’s schemes, as well as from a parametric family of iterative procedures of third- and fourth-order of convergence. We study the local order of convergence of the new iterative methods with memory.
We define each iterative method with memory as a discrete dynamical system and we analyze the stability of the fixed points of its rational operator associated on quadratic polynomials. As far as we know, there is no dynamical study on iterative methods with memory and the techniques of complex dynamics used in schemes without memory are not useful in this context. So, we adapt real multidimensional dynamical tools to afford this task.
The dynamical behavior of Secant method and the versions of Steffensen’ and Traub’s schemes with memory, applied on quadratic polynomials, are analyzed. Different kinds of behavior occur, being in general very stable but pathologic cases as attracting strange fixed points are also found. Finally, a modified parametric family of order four, applied on quadratic polynomials, is also studied, showing the bifurcations diagrams and the appearance of chaos. [-]
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Applied Mathematics and Computation (2015), v. 271,Derechos de acceso
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