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Izv. Saratov Univ. Math. Mech. Inform., 2014, Volume 14, Issue 4(2), Pages 603–608 (Mi isu556)  

Mathematics

Approximation and Reconstruction of Continuous Function with Boundary Conditions

O. I. Shatalina

LOCKO-Bank, 72, Pugacheva str., Saratov, 410056, Russia

Abstract: This work deals with a family of integral operators, which are used to get uniform approximations to continuous function with boundary conditions (stated approximations with the same conditions as well); the Kolmogorov–Nikolsky problem is solved on some compact class. Acquired problem from the theory of ill-posed problems (so-called problem of reconstruction of a continuous function using its mean-root-square approximation) is solved via the goal family of integral operators as well.

Key words: Tikhonov functional, family of integral operators, ill-posed problem, Kolmogorov–Nikolsky problem, uniform approximations.

DOI: https://doi.org/10.18500/1816-9791-2014-14-4-603-608

Full text: PDF file (139 kB)
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Bibliographic databases:

UDC: 517.51

Citation: O. I. Shatalina, “Approximation and Reconstruction of Continuous Function with Boundary Conditions”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(2) (2014), 603–608

Citation in format AMSBIB
\Bibitem{Sha14}
\by O.~I.~Shatalina
\paper Approximation and Reconstruction of Continuous Function with Boundary Conditions
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(2)
\pages 603--608
\mathnet{http://mi.mathnet.ru/isu556}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-603-608}
\elib{https://elibrary.ru/item.asp?id=22625613}


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