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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 726701, 10 pages
Reducing Chaos and Bifurcations in Newton-Type Methods
1Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena, 30202 Cartagena, Spain
2Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
Received 15 October 2012; Revised 25 February 2013; Accepted 16 April 2013
Academic Editor: Shukai Duan
Copyright © 2013 S. Amat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [16 citations]
The following is the list of published articles that have cited the current article.
- Ángel Alberto Magreñán, and José Manuel Gutiérrez, “Real dynamics for damped Newton’s method applied to cubic polynomials,” Journal of Computational and Applied Mathematics, 2013.
- Alicia Cordero, Licheng Feng, Alberto Magreñán, and Juan R. Torregrosa, “A new fourth-order family for solving nonlinear problems and its dynamics,” Journal of Mathematical Chemistry, 2014.
- Angel Alberto Magrenan, “A new tool to study real dynamics: The convergence plane,” Applied Mathematics and Computation, vol. 248, pp. 215–224, 2014.
- A. Alberto Magrenan, Alicia Corder, Jose M. Gutierrez, and Juan R. Torregrosa, “Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane,” Mathematics and Computers in Simulation, vol. 105, pp. 49–61, 2014.
- D.K.R. Babajee, A. Cordero, and J.R. Torregrosa, “Study of iterative methods through the Cayley Quadratic Test,” Journal of Computational and Applied Mathematics, 2014.
- Alicia Cordero, Fazlollah Soleymani, and Juan R. Torregrosa, “Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?,” Applied Mathematics and Computation, vol. 244, pp. 398–412, 2014.
- Wen Zhou, and Jisheng Kou, “Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014.
- Ioannis K. Argyros, and Santhosh George, “Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative,” Applied Mathematics And Computation, vol. 266, pp. 1031–1037, 2015.
- Á. Alberto Magreñán, and Ioannis K. Argyros, “New improved convergence analysis for the secant method,” Mathematics and Computers in Simulation, 2015.
- Ioannis Konstantinos Argyros, and Angel Alberto Magrenan, “On the convergence of inexact two-point Newton-like methods on Banach spaces,” Applied Mathematics And Computation, vol. 265, pp. 893–902, 2015.
- I.K. Argyros, and S.K. Khattri, “Weak convergence conditions for the Newton’s method in Banach space using general majorizing sequences,” Applied Mathematics and Computation, vol. 263, pp. 59–72, 2015.
- Á. Alberto Magreñán, and Ioannis K. Argyros, “New semilocal and local convergence analysis for the Secant method,” Applied Mathematics and Computation, vol. 262, pp. 298–307, 2015.
- Sergio Amat, Sonia Busquier, Concepción Bermúdez, and Á. Alberto Magreñán, “On the election of the damped parameter of a two-step relaxed Newton-type method,” Nonlinear Dynamics, 2015.
- A. Alberto Magrenan, and Ioannis K. Argyros, “Expanding The Applicability Of Secant Method With Applications,” Bulletin Of The Korean Mathematical Society, vol. 52, no. 3, pp. 865–880, 2015.
- Beatriz Campos, Alicia Cordero, Juan R. Torregrosa, and Pura Vindel, “A multidimensional dynamical approach to iterative methods with memory,” Applied Mathematics and Computation, vol. 271, pp. 701–715, 2015.
- Gerardo Honorato, and Sergio Plaza, “Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton's maps,” Applied Mathematics And Computation, vol. 251, pp. 507–520, 2015.