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

A. Berger
  Department of Mathematics and Statistics
  University of Canterbury
  New Zealand
T. P. Hill
  School of Mathematics
  Georgia Institute of Technology

Conditions are given for a $C^k$ 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 $k=\infty$, 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.
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