Geodesic
On Lebesgue constants of local parabolic splines
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 213-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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Lebesgue constants (the norms of linear operators from $C$ to $C$) are calculated exactly for local parabolic splines with an arbitrary arrangement of knots, which were constructed by the second author in 2005, and for N.P. Korneichuk's local parabolic splines, which are exact on quadratic functions. Both constants are smaller than the constants for interpolation parabolic splines.
Keywords: Lebesgue constants; local parabolic splines; arbitrary knots. 
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E. V. Strelkova; V. T. Shevaldin. On Lebesgue constants of local parabolic splines. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 213-219. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a21/

[1] Schurer F., Cheney E.W., “On interpolation cubic splines with equally-spaced nodes”, Proc. Nederlande Acad. van Wetenschappen, 71:5 (1968), 517–524 | MR | Zbl

[2] Richards F., “The Lebesque constants for cardinal spline interpolation”, J. Approx. Theory, 14:2 (1975), 83–92 | DOI | MR | Zbl

[3] Zhensykbaev A.A., “Tochnye otsenki ravnomernogo priblizheniya nepreryvnykh funktsii splainami $r$-go poryadka”, Mat. zametki, 13:2 (1973), 217–228

[4] Tzimbalario J., “Lebesque constants for cardinal $\cal L$-spline interpolation”, Can. J. Math., 29:2 (1977), 441–448 | DOI | MR | Zbl

[5] Morsche H.G. ter, “On the Lebesque constants for cardinal $\cal L$-spline interpolation”, J. Approx. Theory, 45:3 (1985), 232–246 | DOI | MR | Zbl

[6] Subbotin Yu.N., Telyakovskii S.A., “Asimptotika konstant Lebega periodicheskikh interpolyatsionnykh splainov s ravnootstoyaschimi uzlami”, Mat. sb., 191:8 (2000), 131–140 | DOI | MR | Zbl

[7] Subbotin Yu.N., Telyakovskii S.A., “Normy v $L$ periodicheskikh interpolyatsionnykh splainov s ravnootstoyaschimi uzlami”, Mat. zametki, 74:1 (2003), 108–117 | DOI | MR | Zbl

[8] Kim V.A., “Tochnye konstanty Lebega dlya interpolyatsionnykh $\cal L$-splainov tretego poryadka”, Mat. zametki, 84:1 (2008), 59–68 | DOI | MR | Zbl

[9] Kim V.A., “Tochnye konstanty Lebega dlya interpolyatsionnykh $\cal L$-splainov formalno samosopryazhennogo differentsialnogo operatora”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17:3 (2011), 169–177

[10] Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L., Metody splain-funktsii, Nauka, M., 1980, 352 pp. | MR

[11] Lyche T., Schumaker L.L., “Local spline approximation methods”, J. Approx. Theory, 15:4 (1975), 294–325 | DOI | MR | Zbl

[12] Strelkova E.V., Shevaldin V.T., “Lokalnye eksponentsialnye splainy s proizvolnymi uzlami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:1 (2014), 258–263

[13] Korneichuk N.P., Splainy v teorii priblizheniya, Nauka, M., 1984, 352 pp. | MR

[14] Subbotin Yu.N., “Nasledovanie svoistv monotonnosti i vypuklosti pri lokalnoi approksimatsii”, Zhurn. vychisl. matematiki i mat. fiziki, 33:7 (1993), 996–1003 | MR | Zbl

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

[16] Strelkova E.V., Shevaldin V.T., “Formosokhranenie pri approksimatsii lokalnymi eksponentsialnymi splainami proizvolnogo poryadka”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17:3 (2011), 291–299 | MR

[17] Korneichuk N.P., “O priblizhenii lokalnymi splainami minimalnogo defekta”, Ukr. mat. zhurnal, 34:5 (1982), 617–621 | MR