The Convergence Analysis of an Improved Newton-type Method for the Regularization of Nonlinear Ill-Posed Problems
Gui Zhang, Xiqiang Liu, Yan Zhang, Bingyu Kou
Available Online July 2018.
- 10.2991/msam-18.2018.48How to use a DOI?
- nonlinear; ill-posed; operator equations; Newton-type method; convergence
An improved Newton-type iteration method for regularizing the abstract nonlinear ill-posed operator equation is presented and also certain stopping criterion to determine the iteration is proposed in this paper by using the Newton-Landber iteration and the linear Tikhonov regularization. Under the condition that the Fréchet-derivation operator is uniformly boundary and further assumptions on the closeness and smoothness of the exact solution, the local convergence of the approximate solution is obtained.
- © 2018, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Gui Zhang AU - Xiqiang Liu AU - Yan Zhang AU - Bingyu Kou PY - 2018/07 DA - 2018/07 TI - The Convergence Analysis of an Improved Newton-type Method for the Regularization of Nonlinear Ill-Posed Problems BT - Proceedings of the 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018) PB - Atlantis Press SP - 228 EP - 233 SN - 1951-6851 UR - https://doi.org/10.2991/msam-18.2018.48 DO - 10.2991/msam-18.2018.48 ID - Zhang2018/07 ER -