Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 483-494
Citer cet article
V. L. Velikin; N. P. Korneichuk. Accurate estimates of deviations of spline approximations to classes of differentiable functions. Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 483-494. http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/
@article{MZM_1971_9_5_a1,
author = {V. L. Velikin and N. P. Korneichuk},
title = {Accurate estimates of deviations of spline approximations to classes of differentiable functions},
journal = {Matemati\v{c}eskie zametki},
pages = {483--494},
year = {1971},
volume = {9},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/}
}
TY - JOUR
AU - V. L. Velikin
AU - N. P. Korneichuk
TI - Accurate estimates of deviations of spline approximations to classes of differentiable functions
JO - Matematičeskie zametki
PY - 1971
SP - 483
EP - 494
VL - 9
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/
LA - ru
ID - MZM_1971_9_5_a1
ER -
%0 Journal Article
%A V. L. Velikin
%A N. P. Korneichuk
%T Accurate estimates of deviations of spline approximations to classes of differentiable functions
%J Matematičeskie zametki
%D 1971
%P 483-494
%V 9
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/
%G ru
%F MZM_1971_9_5_a1
We derive the approximation on $[0,1]$ of functions $f(x)$ by interpolating spline-functions $s_r(f;x)$ of degree $2r+1$ and defect $r+1$ ($r=1,2,\dots$). Exact estimates for $|f(x)-s_r(f;x)|$ and $\|f(x)-s_r(f;x)\|_C$ on the class $W^mH_\omega$ for $m=1$, $r=1,2,\dots$ and $m=2,3$, $r=2$ for the case of convex $\omega(t)$, are derived.
