References
- Amat , S. , Busquier , S. and Plaza , S. 2004 . Dynamics of a family of third-order iterative methods that do not require using second derivatives . Appl. Math. Comput. , 154 : 735 – 746 .
- Amat , S. , Busquier , S. and Plaza , S. 2005 . Dynamics of the King and Jarratt iterations . Aequationes Math. , 69 : 212 – 223 .
- Amat , S. , Busquier , S. and Plaza , S. 2007 . Dynamics of a family of third-order iterative functions . ANZIAM J , 3 : 343 – 359 .
- Arney , D. C. and Robinson , B. T. 1990 . Exhibiting chaos and fractals with a microcomputer . Comput. Math. Appl. , 19 : 1 – 11 .
- Barna , B. 1956 . Über die Divergenspunkte des Newtonschen Verfahrens zur Bestimmung von Wurzeln algebraischen Gleichungen. II . Publ. Math. Debrecen , 4 : 384 – 397 .
- Beardon , A. F. 1991 . Iteration of Rational Functions . Graduate Texts Mathematics , 132 Springer
- Blanchard , P. 1984 . Complex analytic dynamics on the Riemann sphere . Bull. AMS (new series) , 11 : 85 – 141 .
- Blanchard , P. and Chiu , A. 1991 . “ Complex Dynamics: An Informal Discussion ” . In Fractal Geometry and Analysis , Edited by: Bélair , J. and Dubuc , S. 45 – 98 . Kluwer Academic Publishers .
- Buff , X. and Henriksen , C. 2003 . On the König root-finding algorithms . Nonlinearity , 16 : 989 – 1015 .
- Cayley , A. 1879 . The Newton–Fourier imaginary problem . Am. J. Math. , 2 : 97
- Cayley , A. 1983 . On the Newton–Fourier imaginary problem . Proc. Cambridge Philes. Soc. , 3 : 231 – 232 .
- Cosnard , M. and Masse , C. Convergence presque partout de la méthode de Newton . C.R. Acad. Sci. , 297 549 – 552 .
- Curry , J. H. , Garnett , L. and Sullivan , D. 1983 . On the iteration of a rational function: computer experiment with Newton's method . Comm. Math. Phys. , 91 : 267 – 277 .
- Emerenko , A. and Lyubich , M. 1990 . The dynamics of analytic transformations . Leningrad Math. J , 1 : 563 – 634 .
- Ezquerro , J. A. and Salanova , M. A. 1996 . A note on a family of Newton type iterative processes . Int. J. Comput. Math. , 62 : 223 – 232 .
- Hernández , M. A. and Salanova , M. A. 1994 . A family of Newton type iterative processes . Int. J. Comput. Math. , 51 : 205 – 214 .
- Hurley , M. 1986 . Attracting orbits in Newton method . Trans. AMS , 237 : 143 – 158 .
- C. McMullen, Complex Dynamics and Renormalization. Annals of Mathematics Studies, Princeton University Press, 1994
- J. Milnor, Dynamics in one complex dimension: introductory lectures, preprint #1990/5 (1990), SUNY StonyBrook, Institute for Mathematical Sciences
- Milnor , J. 1999 . Dynamics in One Complex Variable Introductory Lectures , Vieweg .
- Morosawa , S. 1999 . Holomorphic Dynamics , Cambridge University Press .
- Peitgen , H. O. 1989 . Newton's Method and Dynamical Systems , Edited by: Peitgen , H. O. Kluwer Academic Publishers .
- Plaza , S. 2001 . Conjugacy classes of some numerical methods . Proyecciones , 20 : 1 – 17 .
- Roberts , G. E. and Horgan-Kobelski , J. 2004 . Newton's versus Halley's method: an approach via complex dynamics . Int. J. Bifur. Chaos , 14 : 1 – 17 .
- N. Steinmetz, Rational Iteration. de Gruyter Studies in Mathematics, Vol. 16, Walter de Gruyter, 1993
- Varona , J. L. 2002 . Graphics and numerical comparisons between iterative methods . Math. Intelligencer , 24 : 37 – 46 .