A characterisation of Newton maps
Copyright © 2006 Australian Mathematical Society.
NOTE: At the time of publication, the author Theodore Hill was not yet affiliated with Cal Poly.
Conditions are given for a Ck 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, i.e. for k = ∞ , they are also sufficient. The characterisation rests upon the structure of the fixed point set of T and the value of the derivative T1 there, and it is best possible as is demonstrated through examples.
Arno Berger and Theodore P. Hill. "A characterisation of Newton maps" Australian & New Zealand Industrial and Applied Mathematics Journal 48 (2006): 211-223.
Available at: http://works.bepress.com/tphill/65