Iteratively regularized landweber iteration method: Convergence analysis via Hölder Stability

Abstract: In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping satisfies the H\"older stability estimate locally. We consider both noisy as well as non-noisy data in our analysis. Under the a-priori choice of stopping index for noisy data, we show that the iterates remain in a certain ball around exact solution and obtain the convergence rates. The convergence of the Iteratively regularized Landweber iterates to the exact solution is shown under certain assumptions in the case of non-noisy data and as a by-product, under different conditions, two different convergence rates are obtained.