A characterisation of Newton maps

A. Berger, T. P. Hill
2006 ANZIAM journal (Print)  
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, 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 T � there, and it is best possible as is demonstrated through examples.
doi:10.1017/s1446181100003047 fatcat:rgdtwwf3inhyfeqp6lg5t5f2ga