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Diskretnaya Matematika, 2016, Volume 28, Issue 2, Pages 154–160
DOI: https://doi.org/10.4213/dm1378
(Mi dm1378)
 

Modular algorithm for reducing matrices to the Smith normal form

M. A. Cherepnev

Lomonosov Moscow State University
References:
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 $2(n^3\log D)$, where $n$ is the size and $D$ is the determinant (or a multiple of it) of the matrix under consideration.
Keywords: matrix transformation algorithm, normal forms of matrices, complexity of algorithms.
Funding agency Grant number
Russian Foundation for Basic Research офи м2 13-01-12420
This work was supported by the Russian Fund for Basic Research, project 13-01-12420 ofi-m2.
Received: 27.09.2015
English version:
Discrete Mathematics and Applications, 2017, Volume 27, Issue 3, Pages 143–147
DOI: https://doi.org/10.1515/dma-2017-0018
Bibliographic databases:
Document Type: Article
UDC: 519.612
Language: Russian
Citation: M. A. Cherepnev, “Modular algorithm for reducing matrices to the Smith normal form”, Diskr. Mat., 28:2 (2016), 154–160; Discrete Math. Appl., 27:3 (2017), 143–147
Citation in format AMSBIB
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Linking options:
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  • https://doi.org/10.4213/dm1378
  • https://www.mathnet.ru/eng/dm/v28/i2/p154
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