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

DOI

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.

Copyright

© 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/).

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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  -