  Eigenvalue and eigenpair backward errors are computed for matrix pencils
arising in optimal control. In particular, formulas for backward errors are
developed that are obtained under block-structure-preserving and
symmetry-structure-preserving perturbations. It is shown that these eigenvalue
and eigenpair backward errors are sometimes significantly larger than the
corresponding backward errors that are obtained under perturbations that ignore
the special structure of the pencil.
