  The inverse of an $\infty \times \infty$ symmetric band matrix can be
constructed in terms of a matrix continued fraction. For Hamiltonians with
Coulomb plus polynomial potentials, this results in an exact and analytic
Green's operator which, even in finite-dimensional representation, exhibits the
exact spectrum. In this work we propose a finite dimensional representation for
the potential operator such that it retains some information about the whole
Hilbert-space representation. The potential should be represented in a larger
basis, then the matrix should be inverted, then truncated to the desired size,
and finally inverted again. This procedure results in a superb low-rank
representation of the potential operator. The method is illustrated with a
typical nucleon-nucleon potential.
