We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.

翻译：我们认为一种快速的、数据偏差的方向方法,可以实现与Helmholtz内核的点评价有关的矩阵-矢量产品,该方法基于点数组和矩阵的分层分层。考虑的赫尔mholtz内核的多级方向近似,即使在高频水平上也可以有效应用。我们详细分析了所提出的方法几乎线性无症状的复杂性。我们的数字实验与所提供的理论非常一致。