Geodesic
Optimal Recovery of Linear Functionals on Sets of Finite Dimension
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 602-608

Voir la notice de l'article provenant de la source Math-Net.Ru

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 complexity, information operator, information radius, problem complexity, Chebyshev polynomial.
Mots-clés : optimal interpolation 
@article{MZM_2008_84_4_a11,
     author = {S. P. Sidorov},
     title = {Optimal {Recovery} of {Linear} {Functionals} on {Sets} of {Finite} {Dimension}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {602--608},
     publisher = {mathdoc},
     volume = {84},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a11/}
}
TY  - JOUR
AU  - S. P. Sidorov
TI  - Optimal Recovery of Linear Functionals on Sets of Finite Dimension
JO  - Matematičeskie zametki
PY  - 2008
SP  - 602
EP  - 608
VL  - 84
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a11/
LA  - ru
ID  - MZM_2008_84_4_a11
ER  - 
%0 Journal Article
%A S. P. Sidorov
%T Optimal Recovery of Linear Functionals on Sets of Finite Dimension
%J Matematičeskie zametki
%D 2008
%P 602-608
%V 84
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a11/
%G ru
%F MZM_2008_84_4_a11
S. P. Sidorov. Optimal Recovery of Linear Functionals on Sets of Finite Dimension. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 602-608. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a11/