Dynamics of the King and Jarratt iterations

Aequationes Mathematicae

Volumn 69, Issue 3, 2005, Pages 212-223

  Amat, Sergio ^a   Busquier, Sonia ^a   Plaza, Sergio ^b  

^a TECHNICAL UNIVERSITY OF CARTAGENA   (Spain)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Conjugacy classes; Dynamics; Jarratt's iterative method; King's iterative methods; Rational maps

Indexed keywords

EID: 21244492415     PISSN: 00019054     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00010-004-2733-y     Document Type: Article

References (18)

1. I. K. ARGYROS, D. CHEN AND Q. QIAN, The Jarratt method in a Banach space setting, J. Comput. Appl. Math. 51 (1994), 103-106.
2. D. C. ARNEY AND B. T. ROBINSON, Exhibiting chaos and fractals with a microcomputer, Comput. Math. Applic. 19 (3) (1990), 1-11.
3. P. BLANCHARD, Complex Analytic Dynamics on the Riemann Sphere, Bull. Amer. Math. Soc. 11 (1) (1984), 85-141.
4. D. CHEN, On the convergence and optimal error estimates of King's iteration procedures for solving nonlinear equations, Int. J. Comput. Math. 26 (1989), 229-237.
5. J. H. CURRY, L. GARNETT AND D. SULLIVAN, On the iteration of a rational function: computer experiment with Newton's method, Comm. Math. Phys. 91 (1983), 267-277.
6. V. DRAKOPOULOS, N. ARGYROPOULOS AND A. BÖHM, Generalized computation of Schröder iteration functions to motivated families of Julia and Mandelbrot-like sets, SIAM J. Numer. Anal. 36 (1999), 417-435.
7. V. DRAKOPOULOS, On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials, Comput. & Graphics 22 (5) (1998), 629-634.
8. V. DRAKOPOULOS, Schröder iteration functions associated with a one-parameter family of biquadratic polynomials, Chaos Solitons Fractals 13 (2002), 233-243.
9. A. EMERENKO AND M. LYUBICH, The Dynamics of Analytic Transformations, St. Petersburg Math. J. 1 (3) (1990), 563-634.
10. J. A. EZQUERRO, J. M. GUTIÉRREZ, M. A. HERNÁNDEZ AND M. A. SALANOVA, Chebyshevlike methods and quadratic equations, Rev. Anal. Numér. Théor. Approx. 28 (1) (1999), 23-35.
11. M. A. HERNÁNDEZ AND M. A. SALANOVA, Relaxing convergence conditions for the Jarratt method, Southwest J. Pure Appl. Math. 2 (1997), 16-19.
12. P. JARRATT, Some efficient fourth-order multipoint methods for solving equations, BIT 9 (1969), 119-124.
13. R. F. KING, A family of fourth-order methods for nonlinear equations, SIAM J. Numer. Anal. 10 (5) (1973), 876-879.
14. A. M. OSTROWSKI, Solution of Equations and Systems of Equations, Academic Press, New York, 1960.
15. H. O. PEITGEN (ED.), Newton's Method and Dynamical Systems, Kluwer Academic Publishers, 1989.
16. J. F. TRAUB, Iterative Methods for the Solution of Equations, Prentice Hall, Englewood Cliffs, N. J., 1964.
17. E. VRSCAY, Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study, Math. Comp. 46 (173) (1986), 151-169.
18. E. VRSCAY AND W. GILBERT, Extraneous fixed points, basin boundary and chaotic dynamics for Schröder and König rational iteration functions, Numer. Math. 52 (1988), 1-16.