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Conditions of D-Stability of the Fifth-Order Matrices

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Computer Algebra in Scientific Computing (CASC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

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Abstract

The necessary conditions and some sufficient conditions represented in terms of matrix elements have been obtained for the property of D-stability of the fifth-order matrices.

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References

  1. Arrow, K.J., McManus, M.: A note of dynamic stability. Econometrica 26, 448–454 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  2. Svirezhev, Y.M., Logofet, D.O.: Stability of biological communities. Nauka, Moscow (1978) (in Russian)

    Google Scholar 

  3. Johnson, C.R.: Sufficient conditions for D-stability. J. Economic Theory 9, 53–62 (1974)

    Article  MathSciNet  Google Scholar 

  4. Johnson, C.R.: D-stability and Rreal and complex quadratic forms. Lin. Algebra and its Applications 9, 89–94 (1974)

    Article  Google Scholar 

  5. Cross, G.W.: Three types of matrix stability. Lin. Algebra and its Applications. 20, 253–263 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kanovei, G.V., Logofet, D.O.: D-stability of 4-by-4 matrices. J. Comp. Math. and Math. Phys. 38, 1429–1435 (1998)

    MATH  Google Scholar 

  7. Kanovei, G.V., Nephedov, V.N.: On the necessary condition of positiveness for the real polynomial of several variables in the positive orthant. Vestnik Moskovskogo universiteta, vol. 15(2), pp. 24–29. Vytchislitelnaya Mathematika i Kibernetika (2000)

    Google Scholar 

  8. Cain, B.E.: Real, 3×3 D-stable matrices. J. Research Nat. Bureau Standards USA B80(1), 75–77 (1976)

    MathSciNet  MATH  Google Scholar 

  9. Burlakova, L.A.: D-Stable 4th-order matrices. J. Sovremennie technologii. Systemniy analiz. Modelirovanie. 1(21), 109–116 (2009) (in Russian)

    Google Scholar 

  10. Johnson, C.R.: Second, third and fourth order D-Stability. J. Research Nat. Bureau Standards USA B78(1), 11–13 (1974)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 134, Lermontov st., Irkutsk, 664033, Russia

    Larisa A. Burlakova

Authors
  1. Larisa A. Burlakova
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

    Vladimir P. Gerdt

  2. Technische Universität München‘, Institut für Informatik, Garching, Germany

    Ernst W. Mayr

  3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2009 Springer-Verlag Berlin Heidelberg

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Burlakova, L.A. (2009). Conditions of D-Stability of the Fifth-Order Matrices. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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