The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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)
  • Published : 2010.02.28
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Abstract

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].

Keywords

References

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