Fast Multiscale Methods for Solving Ill-Posed Problems via Discrete Dynamical Systems Method

A new multiscale method was developed for numerically solving ill-posed equations of the first kind. This method consists of combining the discrete dynamical systems method with a multiscale projection method. Optimality of the multiscale projection methods was proved on wide classes of ill-posed integral eqations. Finally, numerical experiments are given to illustrate the efficiency of the method.