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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 4, Pages 101–113
DOI: https://doi.org/10.33048/SIBJIM.2020.23.408 (Mi sjim1112) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On integration of a matrix Riccati equation

M. V. Neshchadimab, A. P. Chupakhinca

a Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
b Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
c Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, Novosibirsk 630090, Russia
Full-text PDF (574 kB) Citations (5)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.408
Abstract: We expose the complete integration of the simplest matrix Riccati equation in the two- and three-dimensional cases for an arbitrary linear differential operator. The solution is constructed in terms of the Jordan form of an unknown matrix and the corresponding similarity matrix. We show that a similarity matrix is always representable as the product of two matrices one of which is an invariant of the differential operator.
Keywords: matrix Riccati equation, algebraic invariant, Jordan form. .
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences III.22.4.1
I.1.5.(проект 0314-2019-0011)
The authors were supported by the Programs of Basic Research nos. III.22.4.1 and I.1.5 (project no. 0314-2019-0011) of the Siberian Branch of the Russian Academy of Sciences.
Received: 27.08.2020
Revised: 27.08.2020
Accepted: 10.09.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 4, Pages 732–742
DOI: https://doi.org/10.1134/S1990478920040110
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. V. Neshchadim, A. P. Chupakhin, “On integration of a matrix Riccati equation”, Sib. Zh. Ind. Mat., 23:4 (2020), 101–113; J. Appl. Industr. Math., 14:4 (2020), 732–742
Citation in format AMSBIB
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\by M.~V.~Neshchadim, A.~P.~Chupakhin
\paper On integration of a matrix Riccati equation
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 4
\pages 101--113
\mathnet{http://mi.mathnet.ru/sjim1112}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.408}
\elib{https://elibrary.ru/item.asp?id=44958478}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 4
\pages 732--742
\crossref{https://doi.org/10.1134/S1990478920040110}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85100385214}
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  • https://www.mathnet.ru/eng/sjim/v23/i4/p101
    • This publication is cited in the following 5 articles:
    1. Yu. E. Anikonov, M. V. Neschadim, A. P. Chupakhin, “Mnogomernoe uravnenie Khopfa i nekotorye ego tochnye resheniya”, Sib. zhurn. industr. matem., 25:1 (2022), 5–13  mathnet  crossref  mathscinet
    2. S. A. Vasyutkin, A. P. Chupakhin, “Postroenie minimalnogo bazisa invariantov dlya differentsialnoi algebry (2×2)-matrits”, Sib. zhurn. industr. matem., 25:2 (2022), 21–31  mathnet  crossref  mathscinet
    3. S. A. Vasyutkin, A. P. Chupakhin, “Constructing a Minimal Basis of Invariants for Differential Algebra of 2×2 Matrices”, J. Appl. Ind. Math., 16:2 (2022), 356  crossref
    4. Yu. E. Anikonov, M. V. Neshchadim, A. P. Chupakhin, “Multidimensional Hopf Equation and Some of Its Exact Solutions”, J. Appl. Ind. Math., 16:1 (2022), 1  crossref
    5. M. V. Neshchadim, A. P. Chupakhin, “Method of commutators for integration of a matrix Riccati equation”, J. Appl. Industr. Math., 15:1 (2021), 78–86  mathnet  crossref  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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