About the Kannan-Bachem algorithm
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913571681599488 |
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| author | Sergeraert, Francis |
| author_facet | Sergeraert, Francis |
| contents | The Smith reduction is a basic tool when analyzing integer matrices up to equivalence, and the Kannan-Bachem (KB) algorithm is the first polynomial algorithm computing such a reduction. Using this algorithm in complicated situations where the rank of the studied matrix is not maximal revealed an unexpected obstacle in the algorithm. This difficulty is described, analyzed, a simple solution is given to overcome it, finally leading to a general organization of the KB algorithm, simpler than the original one, efficient and having a general scope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | About the Kannan-Bachem algorithm Sergeraert, Francis Data Structures and Algorithms 15A21 G.4 The Smith reduction is a basic tool when analyzing integer matrices up to equivalence, and the Kannan-Bachem (KB) algorithm is the first polynomial algorithm computing such a reduction. Using this algorithm in complicated situations where the rank of the studied matrix is not maximal revealed an unexpected obstacle in the algorithm. This difficulty is described, analyzed, a simple solution is given to overcome it, finally leading to a general organization of the KB algorithm, simpler than the original one, efficient and having a general scope. |
| title | About the Kannan-Bachem algorithm |
| topic | Data Structures and Algorithms 15A21 G.4 |
| url | https://arxiv.org/abs/2411.02422 |