  Directional interpolation is a fast and efficient compression technique for
high-frequency Helmholtz boundary integral equations, but it requires a very
large amount of storage in its original form. Algebraic recompression can
significantly reduce the storage requirements and speed up the solution process
accordingly. During the recompression process, weight matrices are required to
correctly measure the influence of different basis vectors on the final result,
and for highly accurate approximations, these weight matrices require more
storage than the final compressed matrix. We present a compression method for
the weight matrices and demonstrate that it introduces only a controllable
error to the overall approximation. Numerical experiments show that the new
method leads to a significant reduction in storage requirements.
