Convergence analysis of simplified iteratively regularized Gauss–Newton method in a Banach space setting

Abstract

Iteratively regularized Gauss–Newton method considered by Qinian Jin and Min Zhong (2013), where the iterates are defined by convex optimization problem to get the approximate solution of nonlinear ill-posed equation of the form , where is an operator between Banach spaces X and Y, involves calculation of the derivatives of F at each iterate. In this paper, we suggest a modified form of the iteratively regularized Gauss–Newton method in Banach spaces which requires the derivative of F only at an initial approximation of the solution We study convergence analysis of the method under the same a-posteriori rules as considered by Qinian Jin and Min Zhong (2013). The error estimates for this method are obtained under a modified source condition which also involves the derivative of F only at .

Keywords:

• Nonlinear ill-posed operator equations
• iterative regularization methods
• nonlinear operators on Banach spaces
• source conditions
• stopping index

AMS Subject Classifications:

• Primary: 47A52
• Secondary: 65J15
• 65J22
• 65M30

Acknowledgements

Authors are thankful to Prof. Jin Qinian for providing the MATLAB code which was very useful for the numerical computations done in the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.