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Mat. Zametki, 1991, Volume 50, Issue 6, Pages 85–93 (Mi mz3152)  

This article is cited in 38 scientific papers (total in 38 papers)

Optimal recovery of functionals based on inaccurate data

G. G. Magaril-Il'yaeva, K. Yu. Osipenkob

a Central Scientific-Research Institute of Integrated Automation
b Moscow Aviation Technological Institute

Full text: PDF file (740 kB)

English version:
Mathematical Notes, 1991, 50:6, 1274–1279

Bibliographic databases:

UDC: 517
Received: 12.04.1990

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of functionals based on inaccurate data”, Mat. Zametki, 50:6 (1991), 85–93; Math. Notes, 50:6 (1991), 1274–1279

Citation in format AMSBIB
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\by G.~G.~Magaril-Il'yaev, K.~Yu.~Osipenko
\paper Optimal recovery of functionals based on inaccurate data
\jour Mat. Zametki
\yr 1991
\vol 50
\issue 6
\pages 85--93
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\zmath{https://zbmath.org/?q=an:0778.41018|0745.41034}
\transl
\jour Math. Notes
\yr 1991
\vol 50
\issue 6
\pages 1274--1279
\crossref{https://doi.org/10.1007/BF01158269}
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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. S. N. Kudryavtsev, “Recovery of the values of harmonic functions at a point from their values at other points”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 397–410  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Zhensykbaev, “Spline approximation and optimal recovery of operators”, Russian Acad. Sci. Sb. Math., 80:2 (1995), 393–409  mathnet  crossref  mathscinet  zmath  isi
    3. K. Yu. Osipenko, “On $n$-widths, optimal quadrature formulas, and optimal recovery of functions analytic in a strip”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 55–78  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. K. Yu. Osipenko, “Inequalities for derivatives of functions analytical in a strip”, Math. Notes, 56:4 (1994), 1069–1074  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. V. N. Solov'ev, “Dual extremal problems and their applications to minimax estimation problems”, Russian Math. Surveys, 52:4 (1997), 685–720  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Kolmogorov-type inequalities for derivatives”, Sb. Math., 188:12 (1997), 1799–1832  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. K. Yu. Osipenko, “On optimal recovery methods in Hardy–Sobolev spaces”, Sb. Math., 192:2 (2001), 225–244  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. K. Yu. Osipenko, “Best quadrature formulae on Hardy–Sobolev classes”, Izv. Math., 65:5 (2001), 923–939  mathnet  crossref  crossref  mathscinet  zmath  elib
    10. G. G. Magaril-Il'yaev, K. Yu. Osipenko, V. M. Tikhomirov, “Indefinite Knowledge about an Object and Accuracy of Its Recovery Methods”, Problems Inform. Transmission, 39:1 (2003), 104–118  mathnet  crossref  mathscinet  zmath
    11. G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Optimalnoe vosstanovlenie proizvodnykh na sobolevskikh klassakh”, Vladikavk. matem. zhurn., 5:1 (2003), 39–47  mathnet  mathscinet  zmath  elib
    12. K. Yu. Osipenko, “Optimalnoe vosstanovlenie analiticheskikh funktsii po ikh znacheniyam v ravnomernoi setke na okruzhnosti”, Vladikavk. matem. zhurn., 5:1 (2003), 48–52  mathnet  mathscinet  zmath  elib
    13. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform”, Sb. Math., 195:10 (2004), 1461–1476  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. K. Yu. Osipenko, “O vosstanovlenii resheniya zadachi Dirikhle po netochnym iskhodnym dannym”, Vladikavk. matem. zhurn., 6:4 (2004), 55–62  mathnet  mathscinet  zmath  elib
    15. K. V. Semenikhin, “The optimality of linear estimation algorithms in minimax identification”, Autom. Remote Control, 65:3 (2004), 493–503  mathnet  crossref  mathscinet  zmath  isi
    16. A. V. Bayev, “The Lagrange principle in the problem of optimal inversion of linear operators in finite-dimensional spaces with a priori information about its solution”, Comput. Math. Math. Phys., 47:9 (2007), 1452–1463  mathnet  crossref  mathscinet
    17. K. V. Semenikhin, “Minimax nature of the linear estimates of the indefinite stochastic vector from the generalized probabilistic criteria”, Autom. Remote Control, 68:11 (2007), 1970–1985  mathnet  crossref  mathscinet  zmath  elib  elib
    18. A. V. Bayev, “Optimal recovery and finite-dimensional approximation in linear inverse problems”, Sb. Math., 199:12 (2008), 1735–1750  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. A. V. Bayev, “An optimal regularizing algorithm for the recovery of functionals in linear inverse problems with sourcewise represented solution”, Comput. Math. Math. Phys., 48:11 (2008), 1936–1944  mathnet  crossref  mathscinet  isi
    20. 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
    21. 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
    22. A. V. Baev, “Vychislitelnye algoritmy dlya optimalnykh metodov resheniya lineinykh obratnykh zadach: primenenie optimalnogo vosstanovleniya”, Sib. elektron. matem. izv., 7 (2010), 163–172  mathnet
    23. G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data”, Sb. Math., 203:4 (2012), 569–580  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “How Best to Recover a Function from Its Inaccurately Given Spectrum?”, Math. Notes, 92:1 (2012), 51–58  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    25. E. V. Vvedenskaya, K. Yu. Osipenko, “Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error”, Math. Notes, 92:4 (2012), 473–484  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    26. E. O. Sivkova, “Ob optimalnom vosstanovlenii laplasiana funktsii po ee netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 14:4 (2012), 63–72  mathnet
    27. E. D. Nursultanov, N. T. Tleukhanova, “On reconstruction of multiplicative transformations of functions in anisotropic spaces”, Siberian Math. J., 55:3 (2014), 482–497  mathnet  crossref  mathscinet  isi  elib  elib
    28. 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
    29. R. R. Akopian, “Optimal recovery of an analytic function in a doubly connected domain from its approximately given boundary values”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 13–18  mathnet  crossref  mathscinet  isi  elib
    30. R. R. Akopian, “Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error”, Math. Notes, 99:2 (2016), 177–182  mathnet  crossref  crossref  mathscinet  isi  elib
    31. Osipenko K.Yu., “Optimal Recovery of Operators and Multidimensional Carlson Type Inequalities”, J. Complex., 32:1 (2016), 53–73  crossref  isi
    32. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Exactness and optimality of methods for recovering functions from their spectrum”, Proc. Steklov Inst. Math., 293 (2016), 194–208  mathnet  crossref  crossref  mathscinet  isi  elib
    33. R. R. Akopyan, “Optimal recovery of a function analytic in a disk from approximately given values on a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 25–37  mathnet  crossref  crossref  mathscinet  isi  elib
    34. 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
    35. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary”, Anal. Math., 44:1 (2018), 3–19  crossref  isi
    36. Osipenko K.Yu., “Recovery of Derivatives For Functions Defined on the Semiaxis”, J. Complex., 48 (2018), 111–118  crossref  isi
    37. R. R. Akopyan, “Optimalnoe vosstanovlenie analiticheskoi v poluploskosti funktsii po priblizhenno zadannym znacheniyam na chasti granichnoi pryamoi”, Tr. IMM UrO RAN, 24, no. 4, 2018, 19–33  mathnet  crossref  elib
    38. R. R. Akopyan, “An analogue of the two-constants theorem and optimal recovery of analytic functions”, Sb. Math., 210:10 (2019), 1348–1360  mathnet  crossref  crossref  adsnasa  isi  elib
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