The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 15 Issue 2
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- Pages.111-120
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- 2008
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY $H{\ddot{O}}LDERIAN$ OPERATORS
- Argyros, Ioannis K. (DEPARTMENT OF MATHEMATICAL SCIENCES, CAMERON UNIVERSITY)
- Published : 2008.05.31
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
- Newton's method;
- Banach space;
- locally $H{\ddot{o}}lderian$ operators;
- point-based approximation;
- semilocal convergence;
- successive substitutions;
- fixed point