Open AccessREMARKS ON THE CONVERGENCE OF NEWTON'S METHOD UNDER HÖLDER CONTINUITY CONDITIONS
Author(s) -
Ioannis K. Argyros
Publication year - 1992
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.23.1992.4550
Subject(s) - hölder condition , mathematics , banach space , newton's method , convergence (economics) , fréchet derivative , nonlinear system , ball (mathematics) , mathematical analysis , operator (biology) , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
We use a Newton-like iteration to solve the nonlinear op erator equation in a Banach space. The basic assumption is that the Fréchet-derivative of the nonlinear operator is Hölder continuous on some open ball centered at the initial guess. Under natural assumptions, we prove linear convergence of the iteration to a locally unique solution of the nonlinear equation.