ANZIAM J.
48 (2006), 211223  
A characterisation of Newton maps
 
 
Abstract  
Conditions are given for a
map
T
to be a Newton map, that is, the map associated
with a differentiable realvalued 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.
 
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