한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)
- 제15권4호
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- Pages.365-375
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- 2008
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
A COMPARATIVE STUDY BETWEEN CONVERGENCE RESULTS FOR NEWTON'S METHOD
- Argyros, Ioannis K. (CAMERON UNIVERSITY, DEPARTMENT OF MATHEMATICS SCIENCES) ;
- Hilout, Said (POITIERS UNIVERSITY, LABORATOIRE DE MATHEMATIQUES ET APPLICATIONS)
- 발행 : 2008.11.30
초록
We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.
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