Mixed precision thin SVD algorithms based on the Gram matrix
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908881986256896 |
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| author | Carson, Erin Ma, Yuxin Shao, Meiyue |
| author_facet | Carson, Erin Ma, Yuxin Shao, Meiyue |
| contents | In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and coupling it with a Jacobi algorithm, our theoretical analysis and numerical experiments both indicate that the singular values computed by this mixed precision thin SVD algorithm attain high relative accuracy. In practice, our mixed precision thin SVD algorithm yields speedups of over 10x on a single CPU and about 2x on distributed memory systems when compared with traditional thin SVD methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mixed precision thin SVD algorithms based on the Gram matrix Carson, Erin Ma, Yuxin Shao, Meiyue Numerical Analysis 65F15, 65F25, 65G50, 65Y05, 65Y20 In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and coupling it with a Jacobi algorithm, our theoretical analysis and numerical experiments both indicate that the singular values computed by this mixed precision thin SVD algorithm attain high relative accuracy. In practice, our mixed precision thin SVD algorithm yields speedups of over 10x on a single CPU and about 2x on distributed memory systems when compared with traditional thin SVD methods. |
| title | Mixed precision thin SVD algorithms based on the Gram matrix |
| topic | Numerical Analysis 65F15, 65F25, 65G50, 65Y05, 65Y20 |
| url | https://arxiv.org/abs/2603.11953 |