  We consider the question of approximating the inverse $\mathbf W = \mathbf
V^{-1}$ of the Galerkin stiffness matrix $\mathbf V$ obtained by discretizing
the simple-layer operator $V$ with piecewise constant functions. The block
partitioning of $\mathbf W$ is assumed to satisfy any of the standard
admissibility criteria that are employed in connection with clustering
algorithms to approximate the discrete BEM operator $\mathbf V$. We show that
$\mathbf W$ can be approximated by blockwise low-rank matrices such that the
error decays exponentially in the block rank employed. Similar exponential
approximability results are shown for the Cholesky factorization of $\mathbf
V$.
