  It is shown that, for a Hamiltonian with a band structure, the half width of
local spectral density of states, or strength function, is closely related to
the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the
Wigner-band random-matrix model, making use of a generalized Brillouin-Wigner
perturbation theory, we derive analytical expressions for the width of the NPT
parts under weak and strong perturbation. An iterative algorithm is given, by
which the NPT widths can be computed efficiently, and is used in numerical test
of the analytical predictions.
