ANZIAM  J.  48 (2006), 211-223
A characterisation of Newton maps

 A. Berger   Department of Mathematics and Statistics   University of Canterbury   Christchurch   New Zealand    arno.berger@canterbury.ac.nz
 and
 T. P. Hill   School of Mathematics   Georgia Institute of Technology   Atlanta   USA    hill@math.gatech.edu

Abstract
Conditions are given for a map T to be a Newton map, that is, the map associated with a differentiable real-valued function via Newton's method. For finitely differentiable maps and functions, these conditions are only necessary, but in the smooth case, that is, for , they are also sufficient. The characterisation rests upon the structure of the fixed point set of T and the value of the derivative T' there, and it is best possible as is demonstrated through examples.