Continuity of the direct and inverse problems in one-dimensional scattering theory and numerical solution of the inverse problem

We propose an algorithm for computing the potential V(x) associated to the one-dimensional Schroedinger operator E identical to - d2/dx2 + V(x) -infinite <x< infinite from knowledge of the S.matrix, more exactly, of one of the reelection coefficients. The convergence of the algorithm is guaranteed by the stability results obtained for both the direct and inverse problems