Algorithm xxx: Faster Randomized SVD with Dynamic Shifts
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929313673117696 |
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| author | Feng, Xu Yu, Wenjian Xie, Yuyang Tang, Jie |
| author_facet | Feng, Xu Yu, Wenjian Xie, Yuyang Tang, Jie |
| contents | Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power iteration technique is applied to improve the accuracy of the randomized SVD method. This results in a dynamic shifts based randomized SVD (dashSVD) algorithm, which also collaborates with the skills for handling sparse matrices. An accuracy-control mechanism is included in the dashSVD algorithm to approximately monitor the per vector error bound of computed singular vectors with negligible overhead. Experiments on real-world data validate that the dashSVD algorithm largely improves the accuracy of randomized SVD algorithm or attains same accuracy with fewer passes over the matrix, and provides an efficient accuracy-control mechanism to the randomized SVD computation, while demonstrating the advantages on runtime and parallel efficiency. A bound of the approximation error of the randomized SVD with the shifted power iteration is also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithm xxx: Faster Randomized SVD with Dynamic Shifts Feng, Xu Yu, Wenjian Xie, Yuyang Tang, Jie Mathematical Software Numerical Analysis Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power iteration technique is applied to improve the accuracy of the randomized SVD method. This results in a dynamic shifts based randomized SVD (dashSVD) algorithm, which also collaborates with the skills for handling sparse matrices. An accuracy-control mechanism is included in the dashSVD algorithm to approximately monitor the per vector error bound of computed singular vectors with negligible overhead. Experiments on real-world data validate that the dashSVD algorithm largely improves the accuracy of randomized SVD algorithm or attains same accuracy with fewer passes over the matrix, and provides an efficient accuracy-control mechanism to the randomized SVD computation, while demonstrating the advantages on runtime and parallel efficiency. A bound of the approximation error of the randomized SVD with the shifted power iteration is also proved. |
| title | Algorithm xxx: Faster Randomized SVD with Dynamic Shifts |
| topic | Mathematical Software Numerical Analysis |
| url | https://arxiv.org/abs/2404.09276 |