A characterization of Newton maps. (2005)
Alternative TitleResearch report (University of Canterbury. Dept. of Mathematics and Statistics) ; no. UCDMS2005/11.
Conditions are given for a l 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 can only be necessary, but in the smooth case, i.e. for l=∞, they are also sufficient. The characterization rests upon the structure of the fixed point set of T, and it is best possible as is demonstrated through examples.
KeywordsNewton's method; Newton map; discrete dynamical system; fixed point set; attracting fixed point
ANZSRC Fields of Research01 - Mathematical Sciences
RightsCopyright Arno Berger
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