Geodesic
An asymptotically optimal cubic spline
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 8-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2011_4_a1,
     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},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_4_a1/}
}
TY  - JOUR
AU  - N. K. Bakirov
TI  - An asymptotically optimal cubic spline
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 8
EP  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_4_a1/
LA  - ru
ID  - IVM_2011_4_a1
ER  - 
%0 Journal Article
%A N. K. Bakirov
%T An asymptotically optimal cubic spline
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 8-14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_4_a1/
%G ru
%F IVM_2011_4_a1
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