Geodesic
Approximation by local parabolic splines constructed on the basis of interpolationin the mean
Ural mathematical journal, Tome 3 (2017) no. 1, pp. 81-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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