  It is known that convergence of l.s.b. closed symmetric sesquilinear forms
implies norm resolvent convergence of the associated self-adjoint operators and
this in turn convergence of discrete spectra. In this paper in both cases sharp
estimates for the rate of convergence are derived. An algorithm for the
numerical computation of eigenvalues of generalized Schr\"{o}dinger operators
in $L^2(\mathbb{R})$ is presented and illustrated by explicit examples; the
mentioned general results on the rate of convergence are applied in order to
obtain error estimates for these computations. An extension of the results to
Schr\"{o}dinger operators on metric graphs is sketched.
