Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices. However, due to its low computational intensity, its performance is typically limited by the available memory bandwidth. By optimizing the storage representation of the data within such matrices, this limitation can be lifted and the performance increased. This applies not only to hierarchical matrices but for also for other low-rank approximation schemes, e.g. block low-rank matrices.

翻译：矩阵-向量乘法是众多迭代求解算法的基础，因此对层级矩阵而言同样至关重要。然而，由于其计算密度较低，其性能通常受限于可用内存带宽。通过优化此类矩阵中数据的存储表示方式，这一限制可以得到缓解，进而提升计算性能。这一优化不仅适用于层级矩阵，也适用于其他低秩逼近方案，例如块低秩矩阵。