Then important efforts have been devoted to a "direct solution" of the inverse scattering problem especially by Gelfand and Levitan in the Soviet Union. They proposed an analytic constructive method for determining the solution. When computers became available, some authors have investigated the possibility of applying their approach to similar problems such as the inverse problem in the 1D wave equation. But it rapidly turned out that the inversion is an unstable process: noise and errors can be tremendously amplified making a direct solution hardly practicable.