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Mat. Zametki, 2007, Volume 81, Issue 6, Pages 803–815 (Mi mz3743)  

This article is cited in 11 scientific papers (total in 11 papers)

Optimal Reconstruction of the Solution of the Wave Equation from Inaccurate Initial Data

N. D. Vysk, K. Yu. Osipenko

Moscow State Aviation Technological University

Abstract: In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from $l_2$, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.

Keywords: wave equation, reconstruction problem, information operator, Fourier coefficient, Lagrange function, Lagrange multipliers, the space $l_2$

DOI: https://doi.org/10.4213/mzm3743

Full text: PDF file (441 kB)
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English version:
Mathematical Notes, 2007, 81:6, 723–733

Bibliographic databases:

UDC: 517.5
Received: 09.02.2006

Citation: N. D. Vysk, K. Yu. Osipenko, “Optimal Reconstruction of the Solution of the Wave Equation from Inaccurate Initial Data”, Mat. Zametki, 81:6 (2007), 803–815; Math. Notes, 81:6 (2007), 723–733

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. D. Vysk, “O reshenii volnovogo uravneniya pri netochno zadannykh koeffitsientakh Fure funktsii, zadayuschei nachalnuyu formu struny”, Vladikavk. matem. zhurn., 8:4 (2006), 13–18  mathnet  mathscinet  elib
    2. E. A. Balova, “Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data”, Math. Notes, 82:3 (2007), 285–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Osipenko K. Yu., Wedenskaya E. V., “Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data”, J. Complexity, 23:4–6 (2007), 653–661  crossref  mathscinet  zmath  isi  elib  scopus
    4. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Vvedenskaya E. V., “On the optimal recovery of a solution of a system of linear homogeneous differential equations”, Differ. Equ., 45:2 (2009), 262–266  crossref  mathscinet  zmath  isi  elib  scopus
    6. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. A. V. Arutyunov, S. E. Zhukovskiy, Z. T. Mingaleeva, “Differential properties of the minimum function for diagonalizable quadratic problems”, Comput. Math. Math. Phys., 52:10 (2012), 1342–1350  mathnet  crossref  mathscinet  zmath
    8. N. Temirgaliev, K. E. Sherniyazov, M. E. Berikhanova, “Exact Orders of Computational (Numerical) Diameters in Problems of Reconstructing Functions and Sampling Solutions of the Klein–Gordon Equation from Fourier Coefficients”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S165–S191  mathnet  crossref  crossref  isi  elib
    9. K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Sb. Math., 205:10 (2014), 1442–1472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Babenko V. Babenko Yu. Parfinovych N. Skorokhodov D., “Optimal recovery of integral operators and its applications”, J. Complex., 35 (2016), 102–123  crossref  mathscinet  zmath  isi  elib  scopus
    11. D. B. Bazarkhanov, “Lineinoe vosstanovlenie psevdodifferentsialnykh operatorov na klassakh gladkikh funktsii na m-mernom tore. II”, Tr. IMM UrO RAN, 25, no. 4, 2019, 15–30  mathnet  crossref  elib
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