Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system

Abstract An adaptive multilevel iteration method via a coupled system is proposed, which leads to fast and effective algorithm for solving ill-posed integral equations. In this algorithm, the discrete layer and the iteration can be selected adaptively. By imposing projection conditions, convergence rates of an a priori parameter choice rule and two a posteriori parameter choice rule for this algorithm are established under certain source conditions. Numerical results are presented to illustrate the performance of adaptive multilevel iteration methods with the balance principle and the discrepancy principle, respectively.