nach oben

Journal of Applied and Industrial Mathematics

Erschienen in:

01.11.2020

On Integration of a Matrix Riccati Equation

verfasst von: M. V. Neshchadim, A. P. Chupakhin

Erschienen in: Journal of Applied and Industrial Mathematics | Ausgabe 4/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We execute 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.

Vorheriger Artikel Asymptotic Expansion of the Solution of the Equation of a Slow Axisymmetric Electrovortex Flow Between Two Planes

Nächster Artikel A Parametrization of the General Lorentz Group

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

M. I. Zelikin, Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Faktorial, Moscow, 1998) [in Russian].MATH

F. A. Chernous’ko and V. B. Kolmanovskii, Optimal Control under Random Perturbations (Nauka, Moscow, 1978) [in Russian].MATH

L. V. Ovsyannikov, Lectures on the Fundamentals of Gas Dynamics (Izhevsk Institute of Computer Science, Moscow–Izhevsk, 2003) [in Russian].

A. P. Chupakhin, “Barochronous Gas Motions: General Properties and Submodels of Types \((1,2)\) and \((1,1) \),” Preprint No. 4–98 (Lavrentyev Institute of Hydrodynamics, Novosibirsk, 1998).

A. P. Chupakhin, “Nonbarochronous Submodels of Types \((1,2) \) and \((1,1) \) of the Gas Dynamics Equations,” Preprint No. 1–99 (Lavrentyev Institute of Hydrodynamics, Novosibirsk, 1999).

A. A. Cherevko and A. P. Chupakhin, “The Stationary Ovsyannikov Vortex,” Preprint No. 1–2005 (Lavrentyev Institute of Hydrodynamics, Novosibirsk, 2005).

E. Miller, “A Regularity Criterion for the Navier—Stokes Equation Involving Only the Middle Eigenvalue of the Strain Tensor,” Arch. Rational Mech. Anal. 235, 99–139 (2020).MathSciNetCrossRef

C. A. Stephen and M. W. Gary, “Hierarchies of New Invariants and Conserved Integrals in Inviscid Fluid Flow,” Phys. Fluids 32, 086104 (2020) [https://doi.org/10.1063/5.0011649].

A. G. Fat’yanov, “Some Semianalytical Method for Solution of the Direct Dynamical Problems in Stratified Media,” Dokl. Akad. Nauk SSSR 310 (2), 323–327 (1990).MathSciNet

10.

A. L. Karchevsky, “Analytical Solution of the Maxwell Equations in the Frequency Domain for Horizontal Layered Anisotropic Media,” Geologiya i Geofizika 48 (8), 889–898 (2007).

11.

A. L. Karchevsky and B. R. Rysbayuly, “Analytical Expressions for a Solution of Convective Heat and Moisture Transfer Equations in the Frequency Domain for Layered Media,” Euras. J. Math. Comp. Appl. 3 (4), 55–67 (2015).

12.

A. L. Karchevsky, “Analytical Solutions of the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various Types,” Sibir. Zh. Ind. Mat. 23 (4), 48–68 (2020) [J. Appl. Ind. Math. 14 (4), 648–665 (2020)].MathSciNet

13.

J. Peyrière, “On an Article by W. Magnus on the Fricke Characters of Free Groups,” J. Algebra 228, 659–673 (2020).MathSciNetCrossRef

14.

W. Magnus, “Rings of Fricke Characters and Automorphism Groups of Free Groups,” Math. Zh. 170, 91–103 (1980).MathSciNetCrossRef

15.

C. Procesi, “The Invariant Theory of \(n\times n \) Matrices,” Adv. Math. 19, 306–381 (1976).CrossRef

16.

Yu. P. Razmyslov, “Trace Identities of Complete Matrix Algebras over a Field of Zero Characteristic,” Izv. Akad. Nauk SSSR Ser. Mat. 38 (4), 723–756 (1974) [Math. USSR, Izv. 8, 727–760 (1975)].CrossRef

17.

A. Whittemore, “On Special Linear Characters of Free Groups of Rank \(n\geq 4 \),” Proc. Amer. Math. Soc. 40, 383–388 (1973).MathSciNetMATH

18.

Y. Avishai, D. Berend, and V. Tkachenko, “Trace Maps,” Internat. J. Modern Phys. B. 11, 3525–3542 (1997).MathSciNetCrossRef

19.

M. Bresara, C. Procesi, and S. Spenko, “Quasi-Identities on Matrices and the Cayley–Hamilton Polynomial,” Adv. Math. 280, 439–471 (2015).MathSciNetCrossRef

20.

M. D. Cvetković and L. S. Velimirović, “Application of Shape Operator under Infinitesimal Bending of Surface,” Filomat 33 (4), 1267–1271 (2019).MathSciNetCrossRef

21.

L. S. Velimirović, M. D. Cvetković, M. S. Najdanović, and N. M. Velimirović, “Variation of Operator under Infinitesimal Bending of Surface,” Appl. Math. Comput. 225, 480–486 (2013).MathSciNetMATH

22.

K. K. Brustad, “Total Derivatives of Eigenvalues and Eigenprojections of Symmetric Matrices,” arXiv: 1905.06045v1 [math.AP] 15 May 2019.

23.

N. J. Rose, “On the Eigenvalues of a Matrix Which Commutes with Its Derivative,” Proc. Amer. Math. Soc. 4, 752–754 (1965).MathSciNetCrossRef

24.

I. J. Epstein, “Conditions for a Matrix to Commute with Its Integral,” Proc. Amer. Math. Soc. 14, 266–270 (1963).MathSciNetCrossRef

25.

M. Hausner, “Eigenvalues of Certain Operators on Matrices,” Comm. Pure Appl. Math. 14, 155–156 (1961).MathSciNetCrossRef

26.

F. R Gantmakher, The Theory of Matrices (Fizmatlit, Moscow, 2010; AMS Chelsea Publ., Providence, 1998).

Titel: On Integration of a Matrix Riccati Equation
verfasst von: M. V. Neshchadim
A. P. Chupakhin
Publikationsdatum: 01.11.2020
Verlag: Pleiades Publishing
Erschienen in: Journal of Applied and Industrial Mathematics / Ausgabe 4/2020
Print ISSN: 1990-4789
Elektronische ISSN: 1990-4797
DOI: https://doi.org/10.1134/S1990478920040110

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 4/2020

Variable Neighborhood Search Algorithms for a Competitive Location Problem with Elastic Demand

On Phase Correction in Tomographic Research

Some Approximate Solutions of the Dynamic Problem of Axisymmetric Shock Deformation of a Previously Unstressed Incompressible Elastic Medium

Application of Geodesic Grids for Modeling the Hydrodynamic Processes in Spherical Objects

Asymptotic Expansion of the Solution of the Equation of a Slow Axisymmetric Electrovortex Flow Between Two Planes

Complete Complexity Dichotomy for -Edge Forbidden Subgraphs in the Edge Coloring Problem

Premium Partner

Marktübersichten