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The inverse of an $\infty \times \infty$ symmetric band matrix can beconstructed in terms of a matrix continued fraction. For Hamiltonians withCoulomb plus polynomial potentials, this results in an exact and analyticGreen's operator which, even in finite-dimensional representation, exhibits theexact spectrum. In this work we propose a finite dimensional representation forthe potential operator such that it retains some information about the wholeHilbert-space representation. The potential should be represented in a largerbasis, then the matrix should be inverted, then truncated to the desired size,and finally inverted again. This procedure results in a superb low-rankrepresentation of the potential operator. The method is illustrated with atypical nucleon-nucleon potential.

Approximations of potentials through the truncation of their inverses