Journal of Mathematical Sciences

, Volume 195, Issue 6, pp 791–804 | Cite as

On Tracking Extremum Parameters in the Identification Variational Problem


We compare the problems of tracking extremum parameters in the method of least squares and in the method of variational identification of linear dynamic models for equations with constant coefficients. We derive tracking equations and obtain formulas for the vector of the first order derivatives and the matrix of the second order derivatives of the identification functional with respect to parameters. Bibliography: 5 titles.


Variational Problem Orthogonal Projection Order Derivative Polynomial Approximation Shift Operator 
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  1. 1.
    A. O. Egorshin, “On a method for estimating coefficients of simulating equations for sequences” [in Russian], Sib. Zh. Ind. Mat. 3, No. 2, 78–96 (2000).MathSciNetMATHGoogle Scholar
  2. 2.
    A. O. Egorshin, “Optimization of parameters of stationary models in a unitary space” [in Russian], Avtom. Telemekhanika 65, No. 12, 29–48 (2004); English transl.: Automat. Remote Control. 65, No. 12, 1885–1903 (2004).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    V. I. Kostin, “Extremum points of one function” [in Russian], Upr. Syst. 24, 35–42 (1984).MathSciNetGoogle Scholar
  4. 4.
    V. G. Demidenko, “Reconstruction of the parameters of the homogeneous linear models of the gene network dynamics” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 8, No. 3, 51–59 (2008).MathSciNetMATHGoogle Scholar
  5. 5.
    V. G. Demidenko, “Identification of coefficients of linear difference equations” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 10, No. 2, 45–54 (2010); English transl.: J. Math. Sci., New York 186, No. 3, 407–415 (2012).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics SB RASNovosibirskRussia

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