  We prove optimal convergence estimates for eigenvalues and eigenvectors of a
class of singular/stiff perturbed problems. Our profs are constructive in
nature and use (elementary) techniques which are of current interest in
computational Linear Algebra to obtain estimates even for eigenvalues which are
in gaps of the essential spectrum. Further, we also identify a class of
"regular" stiff perturbations with (provably) good asymptotic properties. The
Arch Model from the theory of elasticity is presented as a prototype for this
class of perturbations. We also show that we are able to study model problems
which do not satisfy this regularity assumption by presenting a study of a
Schroedinger operator with singular obstacle potential.
