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.

翻译：方向插值是一种快速且高效的高频亥姆霍兹边界积分方程压缩技术，但其原始形式需要极大的存储空间。代数再压缩可以显著降低存储需求并加速求解过程。在再压缩过程中，权重矩阵用于正确度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，并证明该方法仅对整体近似引入可控误差。数值实验表明，新方法能够显著降低存储需求。