Sharp Estimates of the Error of Interpolation by Bilinear Splines for Some Classes of Functions
Matematičeskie zametki, Tome 102 (2017) no. 3, pp. 462-469 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For some classes of functions of two variables defined by their moduli of continuity, sharp upper bounds for the approximation of functions by interpolation bilinear splines are obtained.
Keywords: bilinear interpolation spline, modulus of continuity, Steklov function.
@article{MZM_2017_102_3_a10,
     author = {M. Sh. Shabozov and S. N. Mekhmonzoda},
     title = {Sharp {Estimates} of the {Error} of {Interpolation} by {Bilinear} {Splines} for {Some} {Classes} of {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {462--469},
     year = {2017},
     volume = {102},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_3_a10/}
}
TY  - JOUR
AU  - M. Sh. Shabozov
AU  - S. N. Mekhmonzoda
TI  - Sharp Estimates of the Error of Interpolation by Bilinear Splines for Some Classes of Functions
JO  - Matematičeskie zametki
PY  - 2017
SP  - 462
EP  - 469
VL  - 102
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_3_a10/
LA  - ru
ID  - MZM_2017_102_3_a10
ER  - 
%0 Journal Article
%A M. Sh. Shabozov
%A S. N. Mekhmonzoda
%T Sharp Estimates of the Error of Interpolation by Bilinear Splines for Some Classes of Functions
%J Matematičeskie zametki
%D 2017
%P 462-469
%V 102
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_3_a10/
%G ru
%F MZM_2017_102_3_a10
M. Sh. Shabozov; S. N. Mekhmonzoda. Sharp Estimates of the Error of Interpolation by Bilinear Splines for Some Classes of Functions. Matematičeskie zametki, Tome 102 (2017) no. 3, pp. 462-469. http://geodesic.mathdoc.fr/item/MZM_2017_102_3_a10/

[1] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatlit, M., 1960 | MR

[2] B. M. Shumilov, “O lokalnoi approksimatsii bilineinymi splainami”, Vychislitelnye sistemy, 1979, no. 81, 42–47 | MR | Zbl

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

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

[5] V. F. Storchai, “Priblizhenie nepreryvnykh funktsii dvukh peremennykh splain-funktsiyami v metrike $C$”, Issledovaniya po sovremennym problemam summirovaniya i priblizhenii funktsii i ikh prilozheniyam, Dnepropetrovskii gos. un-t, Dnepropetrovsk, 1972, 66–68

[6] S. B. Vakarchuk, “K interpolyatsii bilineinymi splainami”, Matem. zametki, 47:5 (1990), 26–30 | MR | Zbl

[7] M. Sh. Shabozov, “O pogreshnosti interpolyatsii bilineinymi splainami”, Ukr. matem. zhurn., 46:11 (1994), 1554–1560 | MR | Zbl

[8] M. Sh. Shabozov, “Tochnye otsenki odnovremennogo priblizheniya funktsii dvukh peremennykh i ikh proizvodnykh bilineinymi splainami”, Matem. zametki, 59:1 (1996), 142–152 | DOI | MR | Zbl

[9] S. B. Vakarchuk, K. Yu. Myskin, “Nekotorye voprosy odnovremennoi approksimatsii funktsii dvukh peremennykh i ikh proizvodnykh interpolyatsionnymi bilineinymi splainami”, Ukr. matem. zhurn., 57:2 (2005), 147–157 | MR | Zbl

[10] V. N. Malozemov, “Ob otklonenii lomanykh”, Vestn. Leningradskogo un-ta, 1966, no. 7, 150–153 | MR | Zbl

[11] N. P. Korneichuk, Ekstremalnye zadachi teorii priblizheniya, M., Nauka, 1976 | MR