Geodesic
Local approximation by parabolic splines in the mean with large averaging intervals
Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 771-781.

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In the paper, local parabolic splines on the whole real line $\mathbb R$ with equidistant nodes are considered. These splines realize the simplest local approximation scheme, but instead of the function values at the nodes, their average values in symmetric neighborhoods of the nodes are approximated. For an arbitrary averaging step $H$, which more than twice is more than the spline grid step $h$, the approximation errors in the uniform metric for functions and their derivatives are precisely calculated on the class $W_{\infty}^2$. For small steps of averaging $H\leq 2h$, these values were found by E.V.Strelkova in 2007.
Keywords: local approximation, parabolic splines, interpolation in the mean. 
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V. T. Shevaldin. Local approximation by parabolic splines in the mean with large averaging intervals. Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 771-781. http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a11/

[1] Yu. N. Subbotin, “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Priblizhenie funktsii i operatorov, Tr. MIAN SSSR, 138, 1975, 118–173 | MR | Zbl

[2] Yu. N. Subbotin, “Ekstremalnaya funktsionalnaya interpolyatsiya v srednem s naimenshim znacheniem $n$-i proizvodnoi pri bolshikh intervalakh usredneniya”, Matem. zametki, 59:1 (1996), 114–132 | DOI | MR | Zbl

[3] Yu. N. Subbotin, “Ekstremalnaya v $L_p$ interpolyatsiya v srednem pri peresekayuschikhsya intervalakh usredneniya”, Izv. RAN. Ser. matem., 61:1 (1997), 177–198 | DOI | MR | Zbl

[4] A. A. Ligun, A. A. Shumeiko, Asimptoticheskie metody vosstanovleniya krivykh, Izd-vo In-ta matem. NAN Ukrainy, Kiev, 1996

[5] V. T. Shevaldin, “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Ortogonalnye ryady i priblizhenie funktsii, Tr. MIAN SSSR, 164, 1983, 203–240 | MR | Zbl

[6] V. T. Shevaldin, “Ekstremalnaya interpolyatsiya v srednem pri perekryvayuschikhsya intervalakh usredneniya i $L$-splainy”, Izv. RAN. Ser. matem., 62:4 (1998), 201–224 | DOI | MR | Zbl

[7] E. V. Shevaldina, “Approksimatsiya lokalnymi parabolicheskimi splainami funktsii po ikh znacheniyam v srednem”, Tr. IMM UrO RAN, 13, no. 4, 2007, 169–189

[8] H. Behforooz, “Approximation by integro cubic splines”, Appl. Math. Comput., 175:1 (2006), 8–15 | MR | Zbl

[9] H. Behforooz, “Interpolation by integro quintic splines”, Appl. Math. Comput., 216:2 (2010), 364–367 | MR | Zbl

[10] Yu. N. Subbotin, “Nasledovanie svoistv monotonnosti i vypuklosti pri lokalnoi approksimatsii”, Zh. vychisl. matem. i matem. fiz., 33:7 (1993), 996–1003 | MR | Zbl

[11] N. P. Korneichuk, Splainy v teorii priblizheniya, Nauka, M., 1984 | MR | Zbl

[12] V. T. Shevaldin, “Approksimatsiya lokalnymi parabolicheskimi splainami s proizvolnym raspolozheniem uzlov”, Sib. zhurn. vychisl. matem., 8:1 (2005), 77–88 | Zbl