Geodesic
$K$-functionals and best piecewice polynomial approximations
Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 1, pp. 27-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove exact relations between $K$-functionals of pairs $(C,C^l)$ and best uniform piecewice polynomial approximations of functions from $C$. 
@article{MAIS_2007_14_1_a3,
     author = {A. N. Morozov},
     title = {$K$-functionals and best piecewice polynomial approximations},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {27--30},
     year = {2007},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2007_14_1_a3/}
}
TY  - JOUR
AU  - A. N. Morozov
TI  - $K$-functionals and best piecewice polynomial approximations
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2007
SP  - 27
EP  - 30
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MAIS_2007_14_1_a3/
LA  - ru
ID  - MAIS_2007_14_1_a3
ER  - 
%0 Journal Article
%A A. N. Morozov
%T $K$-functionals and best piecewice polynomial approximations
%J Modelirovanie i analiz informacionnyh sistem
%D 2007
%P 27-30
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/MAIS_2007_14_1_a3/
%G ru
%F MAIS_2007_14_1_a3
A. N. Morozov. $K$-functionals and best piecewice polynomial approximations. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 1, pp. 27-30. http://geodesic.mathdoc.fr/item/MAIS_2007_14_1_a3/

[1] R. DeVore, “Degree of approximation”, Approximation Theory 2, Acad. Press, New York, 1976, 117–161 | MR

[2] A. N. Morozov, “Analog teoremy Bernshteina v prostranstve $L_1$”, Matem. zametki, 57:5 (1995), 699–703 | MR | Zbl

[3] A. N. Morozov, “Ob odnom opisanii prostranstv differentsiruemykh funktsii”, Matem. zametki, 70:5 (2001), 758–768 | MR | Zbl

[4] Yu. A. Brudnyi, “Prostranstva, opredelyaemye s pomoschyu lokalnykh priblizhenii”, Tr. MMO, 24, 1971, 69–132 | MR

[5] I. P. Irodova, Svoistva funktsii, zadannykh skorostyu ubyvaniya kusochno-polinomialnoi approksimatsii, sb. nauch. tr., Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, YarGU, Yaroslavl, 1980, 186 pp. | Zbl

[6] G. M. Phillips, “Error estimates for best approximation”, Approximation Theory, Acad. Press, London, 1970, 1–6 | MR

[7] I. Berg, I. Lëfstrëm, Interpolyatsionnye prostranstva. Vvedenie, per. s angl. V. S. Kryuchkova i P. I. Lizorkina, Mir, M., 1980, 264 pp. | MR