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)) )