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Mat. Zametki, 2008, Volume 84, Issue 4, Pages 602–608 (Mi mz6139)  

Optimal Recovery of Linear Functionals on Sets of Finite Dimension

S. P. Sidorov

Saratov State University named after N. G. Chernyshevsky

Abstract: Suppose that $X$ is a linear space and $L_1,…,L_n$ 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 $L_1f,…,L_nf$, $f\in P$.

Keywords: optimal recovery of a linear functional, optimal interpolation, optimal complexity, information operator, information radius, problem complexity, Chebyshev polynomial

DOI: https://doi.org/10.4213/mzm6139

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English version:
Mathematical Notes, 2008, 84:4, 561–567

Bibliographic databases:

UDC: 517.518.85
Received: 10.08.2004
Revised: 25.09.2007

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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