Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 281-294
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N. L. Patsko. Spline approximations in $L_ p$ on an interval. Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 281-294. http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a9/
@article{MZM_1995_58_2_a9,
author = {N. L. Patsko},
title = {Spline approximations in $L_ p$ on an interval},
journal = {Matemati\v{c}eskie zametki},
pages = {281--294},
year = {1995},
volume = {58},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a9/}
}
TY - JOUR
AU - N. L. Patsko
TI - Spline approximations in $L_ p$ on an interval
JO - Matematičeskie zametki
PY - 1995
SP - 281
EP - 294
VL - 58
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a9/
LA - ru
ID - MZM_1995_58_2_a9
ER -
%0 Journal Article
%A N. L. Patsko
%T Spline approximations in $L_ p$ on an interval
%J Matematičeskie zametki
%D 1995
%P 281-294
%V 58
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a9/
%G ru
%F MZM_1995_58_2_a9
We consider approximations in the space $L_p[0,a]$ to differentiable functions whose $l$th derivative belongs to $L_p[0,a]$. The function to be approximated is extended to the entire axis by Lagrange interpolation polynomials, and spline approximation with equally spaced nodes on the entire axis is then applied. This procedure results in a good approximation to the original function.
