Sibirskii Zhurnal Industrial'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Zh. Ind. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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)
References:
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
\Bibitem{NesChu20}
\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}
Linking options:
  • https://www.mathnet.ru/eng/sjim1112
  • 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
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
    Statistics & downloads:
    Abstract page:323
    Full-text PDF :133
    References:54
    First page:7
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025