Geodesic
An asymptotically optimal cubic spline
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 8-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider the interpolation problem for a sufficiently smooth function defined on the segment $[0,1]$. The initial data are values of the mentioned function at given mesh nodes. We construct a cubic spline asymptotically optimal with respect to the growing number of nodes. For the constructed spline we estimate interpolation errors in the uniform and $L_2$ metrics.
Keywords: cubic spline
Mots-clés : interpolation. 
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     author = {N. K. Bakirov},
     title = {An asymptotically optimal cubic spline},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {8--14},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_4_a1/}
}
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N. K. Bakirov. An asymptotically optimal cubic spline. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 8-14. http://geodesic.mathdoc.fr/item/IVM_2011_4_a1/

[1] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | MR | Zbl

[2] Babenko K. I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

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

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

[5] Hall C. A., Meyer W. W., “Optimal error bounds for cubic spline interpolation”, J. Approx. Theory, 16 (1976), 105–122 | DOI | MR | Zbl

[6] Miroshnichenko V. L., “O pogreshnosti priblizheniya interpolyatsionnymi mnogochlenami Lagranzha tretei stepeni”, Vychislitelnye sistemy, 106, Novosibirsk, 1984, 3–24 | MR | Zbl