The main numerical task is to compute eigenvalues and associated eigenfunctions.
Eigenvalues can lie within continuous spectrum.
Good library software has been available for some years and has gradually enlarged the range of SLPs that can be reliably handled. It is now included in Collected Algorithms of the ACM and the supporting articles will shortly appear in ACM Trans. It is simple to replace this collection by another one. The code of the two versions is identical, and has run under a number of Fortran 90 systems.