A characterisation of Newton mapsAustralian & New Zealand Industrial and Applied Mathematics Journal
AbstractConditions 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.
Citation InformationArno Berger and Theodore P. Hill. "A characterisation of Newton maps" Australian & New Zealand Industrial and Applied Mathematics Journal Vol. 48 (2006) p. 211 - 223
Available at: http://works.bepress.com/tphill/65/