Implications of Recompression for Grid-Based Low-Rank Approximation Techniques

Low-rank compression of moment matrix blocks, representing interactions between clusters of vector basis/testing functions, is often done by a rank-revealing analysis of a simplified grid-to-grid interaction matrix, followed by inter/anterpolation and recompression. While this can provide a close estimate of the rank, it can lead to large errors in the compressed representation due to misrepresentation by grids of the underlying relative orientations of the vector functions. The potential hazard is demonstrated via a simplified example for the dyadic formulation.