Geodesic
Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 427-433 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge to the interpolated function and their rate of convergence is of the order of the best approximation of this function.
Keywords: Lagrange interpolation operator, rate of convergence, best approximation, Sobolev space, Hilbert space.
Mots-clés : interpolation polynomial 
@article{MZM_2007_81_3_a10,
     author = {A. I. Fedotov},
     title = {Estimate of the {Norm} of the {Lagrange} {Interpolation} {Operator} in a {Multidimensional} {Sobolev} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {427--433},
     year = {2007},
     volume = {81},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a10/}
}
TY  - JOUR
AU  - A. I. Fedotov
TI  - Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space
JO  - Matematičeskie zametki
PY  - 2007
SP  - 427
EP  - 433
VL  - 81
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a10/
LA  - ru
ID  - MZM_2007_81_3_a10
ER  - 
%0 Journal Article
%A A. I. Fedotov
%T Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space
%J Matematičeskie zametki
%D 2007
%P 427-433
%V 81
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a10/
%G ru
%F MZM_2007_81_3_a10
A. I. Fedotov. Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 427-433. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a10/

[1] A. I. Fedotov, “On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations”, Arch. Math. (Brno), 38:1 (2002), 1–13 | MR | Zbl

[2] M. Teilor, Psevdodifferentsialnye operatory, Mir, M., 1985 | MR | Zbl