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@article{CMFD_2018_64_4_a7,
author = {Kh. M. Shadimetov and A. R. Hayotov and F. A. Nuraliev},
title = {Construction of optimal interpolation formulas in the {Sobolev} space},
journal = {Contemporary Mathematics. Fundamental Directions},
pages = {723--735},
publisher = {mathdoc},
volume = {64},
number = {4},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMFD_2018_64_4_a7/}
}
TY - JOUR AU - Kh. M. Shadimetov AU - A. R. Hayotov AU - F. A. Nuraliev TI - Construction of optimal interpolation formulas in the Sobolev space JO - Contemporary Mathematics. Fundamental Directions PY - 2018 SP - 723 EP - 735 VL - 64 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMFD_2018_64_4_a7/ LA - ru ID - CMFD_2018_64_4_a7 ER -
%0 Journal Article %A Kh. M. Shadimetov %A A. R. Hayotov %A F. A. Nuraliev %T Construction of optimal interpolation formulas in the Sobolev space %J Contemporary Mathematics. Fundamental Directions %D 2018 %P 723-735 %V 64 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMFD_2018_64_4_a7/ %G ru %F CMFD_2018_64_4_a7
Kh. M. Shadimetov; A. R. Hayotov; F. A. Nuraliev. Construction of optimal interpolation formulas in the Sobolev space. Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 64 (2018) no. 4, pp. 723-735. http://geodesic.mathdoc.fr/item/CMFD_2018_64_4_a7/
[1] V. A. Vasilenko, Spline-Functions: Theory, Algorithms, Programs, Nauka, Novosibirsk, 1983 (in Russian) | MR
[2] M. I. Ignat'ev, A. B. Pevniy, “Natural Splines of Many Variables”, Nauka, L., 1991 (in Russian)
[3] P.-J. Laurent, Approximation and Optimization, Mir, Moscow, 1975, (Russian translation)
[4] S. L. Sobolev, Introduction to the Theory of Cubature Formulas, Nauka, Moscow, 1974 (in Russian) | MR
[5] S. B. Stechkin, Yu. N. Subbotin, Splines in Computational Mathematics, Nauka, Moscow, 1976 (in Russian)
[6] Kh. M. Shadimetov, “The discrete analogue of the differential operator $d^{2m}/dx^{2m}$ and its construction”, Questions of Computations and Applied Mathematics, 79, AN UzSSR, Tashkent, 1985, 22–35 (in Russian); Jan. 2010, arXiv: 1001.0556v1[math.NA]
[7] Ahlberg J. H., Nilson E. N., Walsh J. L., The theory of splines and their applications, Academic Press, New York, 1967 | MR | Zbl
[8] Arcangeli R., Lopez de Silanes M. C., Torrens J. J., Multidimensional minimizing splines, Kluwer Academic publishers, Boston, 2004 | MR | Zbl
[9] Attea M., Hilbertian kernels and spline functions, North-Holland, Amsterdam, 1992 | MR
[10] de Boor C., “Best approximation properties of spline functions of odd degree”, J. Math. Mech., 12 (1963), 747–749 | MR | Zbl
[11] de Boor C., A practical guide to splines, Springer, New York–Heidelberg–Berlin, 1978 | MR | Zbl
[12] Holladay J. C., “Smoothest curve approximation”, Math. Tables Aids Comput., 11 (1957), 223–243 | DOI | MR
[13] Mastroianni G., Milovanović G. V., Interpolation processes. Basic theory and applications, Springer, Berlin, 2008 | MR | Zbl
[14] Schoenberg I. J., “On trigonometric spline interpolation”, J. Math. Mech., 13 (1964), 795–825 | MR | Zbl
[15] Schumaker L. L., Spline functions: basic theory, Cambridge University Press, Cambridge, 2007 | MR | Zbl
[16] Shadimetov Kh. M., Hayotov A. R., Nuraliev F. A., “On an optimal quadrature formula in Sobolev space $L_2^{(m)}(0,1)$”, J. Comput. Appl. Math., 243 (2013), 91–112 | DOI | MR | Zbl
[17] Sobolev S. L., “Formulas of mechanical cubature in $n$-dimensional space”, Selected works of S. L. Sobolev, Springer, New York, 2006, 445–450 | DOI | MR
[18] Sobolev S. L., “On interpolation of functions of $n$ variables”, Selected works of S. L. Sobolev, Springer, New York, 2006, 451–456 | DOI | MR
[19] Sobolev S. L., “The coefficients of optimal quadrature formulas”, Selected works of S. L. Sobolev, Springer, New York, 2006, 561–566 | DOI | MR
[20] Sobolev S. L., Vaskevich V. L., The theory of cubature formulas, Kluwer Acad. Publ. Group, Dordrecht, 1997 | MR | Zbl