Modular algorithm for reducing matrices to the Smith normal form
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Mikhail A. Cherepnev
Abstract
The paper gives a complete justification of the modular algorithm for reducing matrices to the Hermitian normal form, which enables one to construct a new modular algorithm for reducing to the Smith normal form that may simultaneously calculate the left matrix of the transformations. The main term in the estimate of the number of operations is 2(n3 log D), where n is the size and D is the determinant (or a multiple of it) of the matrix under consideration.
Originally published in Diskretnaya Matematika (2016) 28, №2, 154-160 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 13-01-12420
Funding statement: This work was supported by the Russian Fund for Basic Research, project 13-01-12420 ofi-m2.
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Bounds for the average-case complexity of monotone Boolean functions
- Modular algorithm for reducing matrices to the Smith normal form
- Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle
- Application of Hadamard product to some combinatorial and probabilistic problems
- Cardinality of subsets of the residue group with nonunit differences of elements
Articles in the same Issue
- Frontmatter
- Bounds for the average-case complexity of monotone Boolean functions
- Modular algorithm for reducing matrices to the Smith normal form
- Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle
- Application of Hadamard product to some combinatorial and probabilistic problems
- Cardinality of subsets of the residue group with nonunit differences of elements
