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Article
A characterisation of Newton maps
Australian & New Zealand Industrial and Applied Mathematics Journal
  • Arno Berger, University of Canterbury
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
Publication Date
1-1-2006
Abstract
Conditions 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 Information
Arno 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/