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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.
Ronald Kriemann (Mon,) studied this question.