Proceedings of the 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018)

The Convergence Analysis of an Improved Newton-type Method for the Regularization of Nonlinear Ill-Posed Problems

Authors
Gui Zhang, Xiqiang Liu, Yan Zhang, Bingyu Kou
Corresponding Author
Gui Zhang
Available Online July 2018.
DOI
https://doi.org/10.2991/msam-18.2018.48How to use a DOI?
Keywords
nonlinear; ill-posed; operator equations; Newton-type method; convergence
Abstract
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.
Open Access
This is an open access article distributed under the CC BY-NC license.

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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  - https://doi.org/10.2991/msam-18.2018.48
ID  - Zhang2018/07
ER  -