Email this article USING THE SMITH FORM FOR THE EXACT MATRIX INVERSION
- Authors: Malaschonok G.I.1
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Affiliations:
- Tambov State University named after G.R. Derzhavin
- Issue: Vol 21, No 6 (2016)
- Pages: 2042-2046
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/365980
- DOI: https://doi.org/10.20310/1810-0198-2016-21-6-2042-2046
- ID: 365980
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Abstract
We discuss the problem of constructing an effective algorithm for computing the inverse matrix for an integer matrix. One of the way, for obtaining the inverse matrix, is based on the matrix Smith form. Known probabilistic algorithm can find the Smith form with the computational bit complexity which has cubic dependence of the matrix sizes. We propose a deterministic extension of this approach to calculating the inverse matrix.
About the authors
Gennadi Ivanovich Malaschonok
Tambov State University named after G.R. Derzhavin
Email: malaschonok@ya.ru
Doctor of Physics and Mathematics, Professor of the Functional Analysis Department Tambov, the Russian Federation
References
Malaschonok G.I. Effective matrix methods in commutative domains. In: D. Krob, A.A. Mikhalev, A.V. Mikhalev (eds.) Formal Power Series and Algebraic Combinatorics // Springer, Berlin, 2000. P. 506-517. Akritas A.G., Malaschonok G.I. Computations in Modules over Commutative Domain // Computer Algebra in Scientific Computing. Springer, Berlin, 2007. P. 11-23. Malaschonok G.I. On computation of kernel of operator acting in a module // Вестник Тамбовского университета. Серия Естественные и технические науки. Тамбов, 2008. Т. 13. Вып. 1. С. 129-131. Malaschonok G.I. Generalized Bruhat decomposition in commutative domains // International Workshop on Computer Algebra in Scientific Computing, LNCS 8136. Springer, Berlin, Heidelberg, 2013. P. 231-242. Malaschonok G., Scherbinin A. Triangular Decomposition of Matrices in a Domain // Computer Algebra in Scientific Computing. LNCS 9301, Springer, Switzerland, 2015. P. 290-304. Storjohann Arne. On the Complexity of Inverting Integer and Polynomial Matrices // Computational Complexity. 2015. V. 24. P. 777-821. doi: 10.1007/s00037-015-0106-7
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