Floating Point Compression of Hierarchical Matrix Formats and its Impact on Matrix-Vector Multiplication
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910003797950464 |
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| author | Kriemann, Ronald |
| author_facet | Kriemann, Ronald |
| contents | Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank compression. However, due to its low computational intensity, the performance of matrix-vector multiplication is typically limited by the available memory bandwidth on parallel systems. With floating point compression the memory footprint can be optimized, which reduces the stress on the memory sub system and thereby increases performance. We will look into the compression of different formats of hierachical matrices and how this can be used to speed up the corresponding matrix-vector multiplication. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floating Point Compression of Hierarchical Matrix Formats and its Impact on Matrix-Vector Multiplication Kriemann, Ronald Distributed, Parallel, and Cluster Computing Mathematical Software 65Y05, 65Y20, 68W10, 68W25, 68P30 Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank compression. However, due to its low computational intensity, the performance of matrix-vector multiplication is typically limited by the available memory bandwidth on parallel systems. With floating point compression the memory footprint can be optimized, which reduces the stress on the memory sub system and thereby increases performance. We will look into the compression of different formats of hierachical matrices and how this can be used to speed up the corresponding matrix-vector multiplication. |
| title | Floating Point Compression of Hierarchical Matrix Formats and its Impact on Matrix-Vector Multiplication |
| topic | Distributed, Parallel, and Cluster Computing Mathematical Software 65Y05, 65Y20, 68W10, 68W25, 68P30 |
| url | https://arxiv.org/abs/2405.03456 |