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Concerning the semilocal convergence of Newton’s method and convex majorants

✍ Scribed by Ioannis K. Argyros


Book ID
107627018
Publisher
Springer Milan
Year
2008
Tongue
Italian
Weight
167 KB
Volume
57
Category
Article
ISSN
0009-725X

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The cubic semilocal convergence on two v
✍ Quan Zheng; Rongxia Bai; Zhongli Liu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 169 KB

In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. Th