On the additional fixed points of schröder iteration functions associated with a one-parameter family of cubic polynomials

Computers and Graphics (Pergamon)

Volumn 22, Issue 5, 1998, Pages 629-634

  Drakopoulos, V ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; MICROCOMPUTERS;

ITERATION FUNCTIONS; ROOTS OF EQUATIONS;

POLYNOMIALS;

EID: 0032180592     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0097-8493(98)00071-5     Document Type: Article

References (11)

1. Schröder, E., Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Mathematische Annalen, 1870, 2, 317-365.
2. Henrici, P., Applied and computational Complex Analysis, Vol 1, Wiley, New York, 1974.
3. Drakopoulos, V., Argiropoulos, N. and Böhm, A., Generalized computation of Schröder iteration functions to motivate families of Julia and Mandelbrot-like sets. SIAM Journal on Numerical Analysis (to appear).
4. Curry, J. H., Garnett, L. and Sullivan, D. R., On the iteration of a rational function: Computer experiments with Newton's method. Communications in Mathematical Physics, 1983, 91, 267-277.
5. Douady, A. and Hubbard, J., On the dynamics of polynomial-like mappings. Annales Scientifiques de l'École Normale Supérieure, 1985, 18, 287-343.
6. Lei, T., Cubic Newton's method of Thurston's type. Preprint.
7. Fatou, M. P., Sur les équations fonctionelles. Bulletin Sociéte Mathématique de France, 1919, 47, 161-271;
8. Fatou, M. P., Bulletin Sociéte Mathématique de France, 1920, 48, 33-94, 208-314.
9. Vrscay, E. R., Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study. Mathematics of Computation, 1986, 46, 151-169.
10. Hoggar, S. G., Mathematics for Computer Graphics, Cambridge University Press, London and New York, 1992.
11. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T., Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York, 1986.