Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but 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.

翻译：方向插值是一种针对高频亥姆霍兹边界积分方程的快速且高效的压缩技术，但其原始形式需要极大的存储空间。代数再压缩能够显著降低存储需求，并相应加速求解过程。在再压缩过程中，需要权重矩阵来正确衡量不同基向量对最终结果的影响；对于高精度近似而言，这些权重矩阵所需的存储空间甚至超过最终压缩矩阵。我们提出了一种针对权重矩阵的压缩方法，并证明该方法仅会在整体近似中引入可控误差。数值实验表明，新方法能够显著降低存储需求。