Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a~differential operator
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 272-280
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We construct local $\mathcal L$-splines with uniform nodes that preserve subsets from the kernel of a linear differential operator $\mathcal L$ of order $r$ with constant real coefficients and pairwise distinct roots of the characteristic polynomial. Pointwise estimates are found for the error of approximation by the constructed $\mathcal L$-splines on classes of functions defined by differential operators of orders smaller than $r$.
Keywords:
approximation, local $\mathcal L$-splines, differential operator.
@article{TIMM_2010_16_4_a25,
author = {E. V. Strelkova and V. T. Shevaldin},
title = {Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a~differential operator},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {272--280},
publisher = {mathdoc},
volume = {16},
number = {4},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a25/}
}
TY - JOUR AU - E. V. Strelkova AU - V. T. Shevaldin TI - Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a~differential operator JO - Trudy Instituta matematiki i mehaniki PY - 2010 SP - 272 EP - 280 VL - 16 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a25/ LA - ru ID - TIMM_2010_16_4_a25 ER -
%0 Journal Article %A E. V. Strelkova %A V. T. Shevaldin %T Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a~differential operator %J Trudy Instituta matematiki i mehaniki %D 2010 %P 272-280 %V 16 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a25/ %G ru %F TIMM_2010_16_4_a25
E. V. Strelkova; V. T. Shevaldin. Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a~differential operator. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 272-280. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a25/