Approximation by local parabolic splines constructed on the basis of interpolationin the mean
Ural mathematical journal, Tome 3 (2017) no. 1, pp. 81-94
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The paper deals with approximative and form–retaining properties of the local parabolic splines of the form $S(x)=\sum\limits_j y_j B_2
(x-jh), \ (h>0),$ where $B_2$ is a normalized parabolic spline with the uniform nodes and functionals $y_j=y_j(f)$ are given for an
arbitrary function $f$ defined on $\mathbb{R}$ by means of the equalities $$y_j=\frac{1}{h_1}\int\limits_{\frac{-h_1}{2}}^{\frac{h_1}{2}}
f(jh+t)dt \quad (j\in\mathbb{Z}). $$ On the class $W^2_\infty$ of functions under $0$, the approximation error value is
calculated exactly for the case of approximation by such splines in the uniform metrics.
Keywords:
Local parabolic splines, Approximation, Mean.
@article{UMJ_2017_3_1_a7,
author = {Elena V. Strelkova},
title = {Approximation by local parabolic splines constructed on the basis of interpolationin the mean},
journal = {Ural mathematical journal},
pages = {81--94},
publisher = {mathdoc},
volume = {3},
number = {1},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a7/}
}
TY - JOUR AU - Elena V. Strelkova TI - Approximation by local parabolic splines constructed on the basis of interpolationin the mean JO - Ural mathematical journal PY - 2017 SP - 81 EP - 94 VL - 3 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a7/ LA - en ID - UMJ_2017_3_1_a7 ER -
Elena V. Strelkova. Approximation by local parabolic splines constructed on the basis of interpolationin the mean. Ural mathematical journal, Tome 3 (2017) no. 1, pp. 81-94. http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a7/