• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.13-18
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• 2009

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권2호
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• pp.111-120
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• 2008

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.