  In a 1990 paper Helton and Young showed that under certain conditions the
optimal solution of the Nehari problem corresponding to a finite rank Hankel
operator with scalar entries can be efficiently approximated by certain
functions defined in terms of finite dimensional restrictions of the Hankel
operator. In this paper it is shown that these approximants appear as optimal
solutions to restricted Nehari problems. The latter problems can be solved
using relaxed commutant lifting theory. This observation is used to extent the
Helton and Young approximation result to a matrix-valued setting. As in the
Helton and Young paper the rate of convergence depends on the choice of the
initial space in the approximation scheme.
