A convergence analysis of regularization by discretization in preimage space (Q2840002)

The paper studies inverse problems formulated as linear or nonlinear ill-posed operator equations in Hilbert spaces and their regularization by restriction to a sequence of finite-dimensional subspaces in the preimage space (least squares projection). As opposed to discretization of the image space (dual least squares projection), which under reasonable assumptions always leads to convergence, counterexamples show that the least squares projection does not always converge. The paper shows convergence results under certain conditions on the solution. New aspects are the use of the discrepancy principle for the choice of the subspace and the treatment of nonlinear problems.