ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY <TEX>$H{\ddot{O}}LDERIAN$</TEX> OPERATORS
ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H?OLDERIAN OPERATORS
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.2, pp.111-120
Argyros, Ioannis K.
(DEPARTMENT OF MATHEMATICAL SCIENCES, CAMERON UNIVERSITY)
Argyros, Ioannis K..
(2008). ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY <TEX>$H{\ddot{O}}LDERIAN$</TEX> OPERATORS. 한국수학교육학회지시리즈B:순수및응용수학, 15(2), 111-120.
Abstract
A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.
- keywords
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Newton's method,
Banach space,
locally <tex> $H{\ddot{o}}lderian$</tex> operators,
point-based approximation,
semilocal convergence,
successive substitutions,
fixed point