Numerical solution of forward and inverse Sturm-Liouville problems with an angular momentum singularity

This paper considers analytical and numerical-analytical issues encountered in the solution of an inverse Sturm-Liouville problem with a Bessel-type singularity. The main results are as follows: (i) there is a wide class of numerical methods for eigenvalue calculation which are not adversely affected by this type of singularity; (ii) a simple least-squares technique proposed by Röhrl in the regular case can actually be implemented in an even simpler way, and still work just as effectively; (iii) in some cases, a 'unique local minimizer' result of the type obtained by Röhrl is still available; (iv) finite spectral data and noise remain the most serious obstacles to accurate reconstruction.