A convergence analysis of an inexact Newton-Landweber iteration method for nonlinear problem

ABSTRACT

In this paper, we study the convergence and the convergence rates of an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. Opposed to the traditional methods, we analyze an inexact Newton–Landweber iteration depending on the Hölder continuity of the inverse mapping when the data are not contaminated by noise. With the namely Hölder-type stability and the Lipschitz continuity of DF, we prove convergence and monotonicity of the residuals defined by the sequence induced by the iteration. Finally, we discuss the convergence rates.

KEYWORDS:

• Nonlinear problem
• convergence rates
• the Newton–Landweber iteration
• Hölder-type stability

AMS SUBJECT CLASSIFICATIONS:

• 65R20
• 68W25
• 65F22

Acknowledgements

The authors gratefully acknowledge Professor Jinyuan Du for his assistance and extremely instructive suggestion in this research.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project is supported by the National Natural Science Foundation of China [grant number 61271398]; K. C. Wong Magna Fund in Ningbo University; Scientific Research Foundation of Graduate School of Ningbo University [grant number G17068].