The approximate inverse in action II: convergence and stability

The approximate inverse is a scheme for constructing stable inversion formulas for operator equations. Originally, it is defined on L 2 L^2 -spaces. In the present article we extend the concept of approximate inverse to more general settings which allow us to investigate the discrete version of the approximate inverse which actually underlies numerical computations. Indeed, we show convergence if the discretization parameter tends to zero. Further, we prove stability, that is, we show the regularization property. Finally we apply the results to the filtered backprojection algorithm in 2D-tomography to obtain convergence rates.