Improved local convergence analysis of the Landweber iteration in Banach spaces

The convergence analysis of the Landweber iteration for solving inverse problems in Banach spaces via Hölder stability estimates is well studied by de Hoop et al. (Inverse Probl 28(4):045001, 2012) in the presence of unperturbed data. For real life problems, it is important to study the convergence analysis in the presence of perturbed data. In this paper, we show that the convergence analysis of the Landweber iteration can also be studied by utilizing the Hölder stability estimates in the presence of perturbed data. Furthermore, as a by-product, we formulate the convergence rates of the Landweber iteration without utilizing any additional smoothness condition. This shows the advantage of Hölder stability estimates over a tangential cone condition in the theory of inverse problems.