한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제17권1호
  • /
  • Pages.1-27
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  • 2010
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지

ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREE

  • Argyros, Ioannis K. (CAMERON UNIVERSITY, DEPARTMENT OF MATHEMATICS SCIENCES) ;
  • Hilout, Said (POITIERS UNIVERSITY, LABORATORIE DE MATHEMATIQUES ET APPLICATIONS)
  • 발행 : 2010.02.28
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⟨ 이전 논문 다음 논문 ⟩

초록

Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].

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참고문헌

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