Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


by Xavier Buff
Laboratoire de Mathematiques Emile Picard
Universite Paul Sabatier,
Toulouse, France

MIDIT-seminar 472

Wednesday March 01, 2000, 11.00 h
at MIDIT, MAT, Bldg. 303, Room 026, DTU,

Abstract: A well known algorithm to find the roots of a polynomial is the Newton's method. I will present a variant due to the astronomer that discovered the comet. Instead of approximating P by its tangent, one can approximate P by the Moebius transformation that best oscullates P.
One then has to iterate the rational map
H_P(z) = z - P(z)/ ( P'(z) - P(z)P''(z)/(2P'(z)) )