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Berger, A and Hill, TP (2006)

A characterisation of Newton maps

ANZIAM J. 48, pp. 211-223.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

Abstract: Conditions are given for a Ck map T to be a Newton map, that is, the map associated with a differentiable realvalued function via Newton’s method. For finitely differentiable maps and functions, these conditions are only necessary, but in the smooth case, that is, 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.

@article {, AUTHOR = {Berger, Arno and Hill, Theodore P.}, TITLE = {A characterisation of Newton maps}, JOURNAL = {ANZIAM J. }, YEAR = {2006}, VOLUME = {8}, NUMBER = {}, PAGES = {211--223}, DOI = {}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Analysis, Dynamical Systems