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Journal of Mathematical Sciences

, Volume 189, Issue 4, pp 596–603 | Cite as

On Optimal Recovery of Solutions to Difference Equations from Inaccurate Data

  • G. G. Magaril-Il’yaev
  • K. Yu. Osipenko
Article

We prove a theorem on the optimal recovery of powers of a normal operator. To illustrate the result, we prove assertion concerning the optimal recovery of the temperature of a body in the difference model of the heat equation and the optimal recovery of a solution in the difference model of a system of ordinary differential equations. Bibliography: 6 titles.

Keywords

Orthonormal Basis Heat Equation Normal Matrix Admissible Function Optimal Recovery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    E. V. Vvedenskaya, “On optimal recovery of a solution to the heat equation from inaccurate given temperature at different time moments” [in Russian], Vladikavkaz. Math. Zh. 8, No. 1, 16–21 (2006).MathSciNetGoogle Scholar
  2. 2.
    K. Yu. Osipenko and E. W. Wedenskaya (E. V. Vvedenskaya), “Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data,” J. Complexity 23, No. 4–6, 653–661 (2007).MathSciNetMATHCrossRefGoogle Scholar
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    G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data” [in Russian], Mat. Sb. 200, No. 5, 37–54 (2009); English transl.: Sb. Math. 200, No. 5, 665–682 (2009).MathSciNetMATHCrossRefGoogle Scholar
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    E. V. Vvedenskaya, “On the optimal recovery of a solution of a system of linear homogeneous differential equations” [in Russian], Differ. Uravn. 45, No. 2, 255–259 (2009); English transl.: Differ. Equ. 45, No. 2, 262–266 (2009).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.A. A. Kharkevich Institute for Information Transmission Problems RASMoscowRussia
  3. 3.South Mathematical Institute of VSC RASVladikavkazRussia

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