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