Influence of the order between discretization and regularization in solving ill-posed problems

Abstract

Discretization and regularization are required steps to provide a stable approximation when solving integral equations of the first kind. The integral operator involved may be approximated by a sequence of finite rank operators and then the regularization procedure is applied. On the other hand, a regularization procedure can be conceived prior to the discretization. Both approaches are developed, implemented and compared for certain projection based methods.