ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREE
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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 Theorem1 and the two examples given in [17], and then, we provide the proof in affine invariant form forth is result. Then, we also establish new conver-gence 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 otherfail[17].
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 Theorem1 and the two examples given in [17], and then, we provide the proof in affine invariant form forth is result. Then, we also establish new conver-gence 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 otherfail[17].
참고문헌 (17)
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