Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space
For researchers in inverse problems, this provides a more robust and efficient iterative regularization method, though it is an incremental improvement over existing work.
The paper proposes a unified parameter choice strategy for Newton-Landweber iterations in Banach space that ensures both convergence and convergence rates, achieving strong convergence as noise tends to zero even without additional regularity, and demonstrates improved efficiency over prior methods.
This paper is a close follow-up of Kaltenbacher and Tomba 2013 and Jin 2012, where Newton-Landweber iterations have been shown to converge either (unconditionally) without rates or (under an additional regularity assumption) with rates. The choice of the parameters in the method were different in each of these two cases. We now found a unified and more general strategy for choosing these parameters that enables both convergence and convergence rates. Moreover, as opposed to the previous one, this choice yields strong convergence as the noise level tends to zero, also in the case of no additional regularity. Additionally, the resulting method appears to be more efficient than the one from Kaltenbacher and Tomba 2013, as our numerical tests show.