A Low-Rank BUG Method for Sylvester-Type Equations
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908625363009536 |
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| author | Vretinaris, Georgios |
| author_facet | Vretinaris, Georgios |
| contents | We introduce a low-rank algorithm inspired by the Basis-Update and Galerkin (BUG) integrator to efficiently approximate solutions to Sylvester-type equations. The algorithm can exploit both the low-rank structure of the solution as well as any sparsity present to reduce computational complexity. Even when a standard dense solver, such as the Bartels-Stewart algorithm, is used for the reduced Sylvester equations generated by our approach, the overall computational complexity for constructing and solving the associated linear systems reduces to O(kr(n^2+m^2 +mn + r^2)), for X in R^{m \times n}, where k is the number of iterations and r the rank of the approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Low-Rank BUG Method for Sylvester-Type Equations Vretinaris, Georgios Numerical Analysis 14J60 (Primary) 14F05, 14J26 (Secondary) We introduce a low-rank algorithm inspired by the Basis-Update and Galerkin (BUG) integrator to efficiently approximate solutions to Sylvester-type equations. The algorithm can exploit both the low-rank structure of the solution as well as any sparsity present to reduce computational complexity. Even when a standard dense solver, such as the Bartels-Stewart algorithm, is used for the reduced Sylvester equations generated by our approach, the overall computational complexity for constructing and solving the associated linear systems reduces to O(kr(n^2+m^2 +mn + r^2)), for X in R^{m \times n}, where k is the number of iterations and r the rank of the approximation. |
| title | A Low-Rank BUG Method for Sylvester-Type Equations |
| topic | Numerical Analysis 14J60 (Primary) 14F05, 14J26 (Secondary) |
| url | https://arxiv.org/abs/2511.01735 |