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On the local convergence of inexact Newton-type methods under residual control-type conditions

✍ Scribed by Hongmin Ren; Ioannis K. Argyros

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
322 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

A local convergence analysis of inexact Newton-type methods using a new type of residual control was recently presented by C. Li and W. Shen. Here, we introduce the center-Hölder condition on the operator involved, and use it in combination with the Hölder condition to provide a new local convergence analysis with the following advantages: larger radius of convergence, and tighter error bounds on the distances involved. These results are obtained under the same hypotheses and computational cost. Numerical examples further validating the theoretical results are also provided in this study.

📜 SIMILAR VOLUMES

Local convergence of inexact methods und
Local convergence of inexact methods under the Hölder condition
✍ Chong Li; Weiping Shen 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 816 KB

We study the convergence properties for some inexact Newton-like methods including the inexact Newton methods for solving nonlinear operator equations on Banach spaces. A new type of residual control is presented. Under the assumption that the derivative of the operator satisfies the Hölder conditio