Compressing a Fast Multipole Method Representation of an Integral Equation Matrix

It has been observed that the memory requirements associated with $H^{2}$ representations of integral equation matrices can be reduced by incorporating translational invariance. This can be accomplished for a non-translationally invariant $\boldsymbol{H}^{2}$ representation using a left/right iterative algorithm. In this paper, it is shown that a similar algorithm can also be used to compress an existing fast multipole method (FMM). It is observed that the iterative compression converges faster when used to compress an FMM than when it is applied to an $\boldsymbol{H}^{2}$ representation.