Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911098136952832 |
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| author | Li, Yingzhou Liu, Jingyu |
| author_facet | Li, Yingzhou Liu, Jingyu |
| contents | In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierarchical matrix, with the low-rank blocks replaced by Tucker low-rank blocks. Using high-dimensional interpolation as well as tensor contractions, algorithms for the construction and matrix-vector multiplication of HTLR matrices are proposed admitting linear and quasi-linear complexities respectively. Numerical experiments demonstrate that the HTLR matrix performs well in both memory and runtime. Furthermore, the HTLR matrix can also be applied on quasi-uniform grids in addition to uniform grids, enhancing its versatility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication Li, Yingzhou Liu, Jingyu Numerical Analysis In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierarchical matrix, with the low-rank blocks replaced by Tucker low-rank blocks. Using high-dimensional interpolation as well as tensor contractions, algorithms for the construction and matrix-vector multiplication of HTLR matrices are proposed admitting linear and quasi-linear complexities respectively. Numerical experiments demonstrate that the HTLR matrix performs well in both memory and runtime. Furthermore, the HTLR matrix can also be applied on quasi-uniform grids in addition to uniform grids, enhancing its versatility. |
| title | Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.05958 |