Numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators

A new numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators from their spectral characteristics is developed. The method was tested on the problems for perturbed Sturm–Liouville operator. The results of numerous calculations have shown its computational efficiency. The simple algebraic formulas for finding the eigenvalues of discrete operators was found. At that the calculation of eigenvalues of perturbed self-adjoint operator can start from any number, no matter known the eigenvalues from previous numbers or not.