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Matematicheskie Zametki, 2008, Volume 84, Issue 4, Pages 602–608
DOI: https://doi.org/10.4213/mzm6139
(Mi mzm6139)
 

Optimal Recovery of Linear Functionals on Sets of Finite Dimension

S. P. Sidorov

Saratov State University named after N. G. Chernyshevsky
References:
Abstract: Suppose that $X$ is a linear space and $L_1,\dots,L_n$ is a system of linearly independent functionals on $P$, where $P\subset X$ is a bounded set of dimension $n+1$. Suppose that the linear functional $L_0$ is defined in $X$. In this paper, we find an algorithm that recovers the functional $L_0$ on the set $P$ with the least error among all linear algorithms using the information $L_1f,\dots,L_nf$, $f\in P$.
Keywords: optimal recovery of a linear functional, optimal interpolation, optimal complexity, information operator, information radius, problem complexity, Chebyshev polynomial.
Received: 10.08.2004
Revised: 25.09.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 4, Pages 561–567
DOI: https://doi.org/10.1134/S0001434608090289
Bibliographic databases:
UDC: 517.518.85
Language: Russian
Citation: S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Mat. Zametki, 84:4 (2008), 602–608; Math. Notes, 84:4 (2008), 561–567
Citation in format AMSBIB
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