Chaos in King’s iterative family

Applied Mathematics Letters - Tập 26 Số 8 - Trang 842-848 - 2013
Alicia Cordero1, Javier G. Maimó2, Juan R. Torregrosa1, María P. Vassileva2, P. Vindel3
1Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain
2Instituto Tecnológico de Santo Domingo, Santo Domigo, Dominican Republic
3Instituto de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, Campus de Riu Sec s/n, Castellón, Spain#TAB#

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Tài liệu tham khảo

Varona, 2002, Graphic and numerical comparison between iterative methods, Math. Intelligencer, 24, 37, 10.1007/BF03025310

Amat, 2004, Review of some iterative root-finding methods from a dynamical point of view, Sci. Ser. A Math. Sci. (N.S.), 10, 3

Gutiérrez, 2010, Dynamics of a new family of iterative processes for quadratic polynomials, J. Comput. Appl. Math., 233, 2688, 10.1016/j.cam.2009.11.017

Honorato, 2011, Dynamics of a high-order family of iterative methods, J. Complexity, 27, 221, 10.1016/j.jco.2010.10.005

Chicharro, 2013, Complex dynamics of derivative-free methods for nonlinear equations, Appl. Math. Comput., 219, 7023

S. Artidiello, F. Chicharro, A. Cordero, J.R. Torregrosa, Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods, Int. J. Comput. Math. http://dx.doi.org/10.1080/00207160.2012.748900.

Scott, 2011, Basin attractors for various methods, Appl. Math. Comput., 218, 2584

Chun, 2012, On optimal fourth-order iterative methods free from second derivative and their dynamics, Appl. Math. Comput., 218, 6427

Neta, 2012, Basin attractors for various methods for multiple roots, Appl. Math. Comput., 218, 5043

King, 1973, A family of fourth-order methods for nonlinear equations, SIAM J. Numer. Anal., 10, 876, 10.1137/0710072

Ostrowski, 1964

Amat, 2005, Dynamics of the King and Jarratt iterations, Aequationes Math., 69, 212, 10.1007/s00010-004-2733-y

Blanchard, 1994, The dynamics of Newton’s method, Proc. Sympos. Appl. Math., 49, 139, 10.1090/psapm/049/1315536

Smale, 1985, On the efficiency of algorithms of analysis, Bull. Allahabad Math. Soc., 13, 87, 10.1090/S0273-0979-1985-15391-1

McMullen, 1987, Family of rational maps and iterative root-finding algorithms, Ann. of Math., 125, 467, 10.2307/1971408

Blanchard, 1984, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc., 11, 85, 10.1090/S0273-0979-1984-15240-6

Devaney, 1999, The Mandelbrot set, the Farey tree and the Fibonacci sequence, Amer. Math. Monthly, 106, 289, 10.2307/2589552