On a noisy operator equation and the identification of point-sources in the 1-D wave equation

We consider a linear operator equation with noise in the operator and the r ight-hand side. As a concept, the ill-posed ness of the problem is composed of the ill-posedness with respect to the operator and the ill-posedness wi th respect to the right-hand side. Starting at a numerical procedure Sor ex act data, in the case of noisy data a numerical procedure and error estimat es are given. As an example, a Volterra integral equation of the first kind is investigated and finally applied to a point source reconstruction probl em for the wave equation. The method is tested by numerical experiments.