Reconstruction of potentials in the Sturm-Liouville inverse problem by the variational method

An algorithm for solving the inverse Sturon-Liouville (SL) problem was suggested. The problem deals with the reconstruction of a functional dependence for the potential function from observable eigenvalues. The variational method was employed for the reconstruction of potentials in the SL problem. The analysis showed that the algorithm involves an automatic self-regularization of eigenfunctions.