Geodesic
On simultaneous approximation of functions of two variables and their derivatives by bilinear interpolation splines
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 2, pp. 60-72 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper an exact error value of simultaneous approximation of functions of two variables and their partial derivatives by bilinear interpolation splines on some classes of functions defined by the modulus of continuity is founded.
Keywords: approximation of function, bilinear interpolation splines, modulus of continuity. 
@article{VNGU_2018_18_2_a5,
     author = {M. Sh. Shabozov and U. N. Zevarshoev},
     title = {On simultaneous approximation of functions of two variables and their derivatives by bilinear interpolation splines},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {60--72},
     year = {2018},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_2_a5/}
}
TY  - JOUR
AU  - M. Sh. Shabozov
AU  - U. N. Zevarshoev
TI  - On simultaneous approximation of functions of two variables and their derivatives by bilinear interpolation splines
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2018
SP  - 60
EP  - 72
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VNGU_2018_18_2_a5/
LA  - ru
ID  - VNGU_2018_18_2_a5
ER  - 
%0 Journal Article
%A M. Sh. Shabozov
%A U. N. Zevarshoev
%T On simultaneous approximation of functions of two variables and their derivatives by bilinear interpolation splines
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2018
%P 60-72
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2018_18_2_a5/
%G ru
%F VNGU_2018_18_2_a5
M. Sh. Shabozov; U. N. Zevarshoev. On simultaneous approximation of functions of two variables and their derivatives by bilinear interpolation splines. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 2, pp. 60-72. http://geodesic.mathdoc.fr/item/VNGU_2018_18_2_a5/

[1] B. M. Shumilov, “Local approximation by bilinear splines”, Metody Splayn-Funktsiy (Vychislitel'nye Sistemy), 81 (1979), 42–47 (in Russian) | Zbl

[2] Y. S. Zavyalov, B. I. Kvasov, V. L. Miroshnichenko, Mehtods of Spline Functions, Nauka, M., 1980 (in Russian) | MR

[3] S. B. Vakarchuk, “Interpolation by bilinear splines”, Math. Notes, 47:5 (1990), 441–444 | DOI | MR | Zbl

[4] M. Sh. Shabozov, “On the error of the interpolation by bilinear splines”, Ukr. Math. J., 46:11 (1994), 1719–1726 | DOI | MR | Zbl

[5] M. Sh. Shabozov, “Exact bounds for simultaneous approximation of functions of two variables and their derivatives by bilinear splines”, Math. Notes, 59:1 (1996), 104–111 | DOI | DOI | MR | Zbl

[6] S. B. Vakarchuk, K. Yu. Miskin, “Some problems of simultaneous approximation of functions of two variables and their derivatives by interpolation bilinear splines”, Ukr. Math. J., 57:2 (2005), 173–185 | MR | Zbl

[7] J. H. Ahlberg, E. N. Nilson, J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, N. Y.–London, 1967 | MR | Zbl

[8] S. B. Stechkin, Yu. N. Subbotin, Splines in Calculus Mathematics, Nauka, M., 1976 (in Russian)

[9] N. P. Korneichuk, The Splines in Theory of Approximation, Nauka, M., 1984 (in Russian) | MR

[10] V. F. Storchay, “Approximating the continuous functions of two variables by spline functions in metric $\mathbb{C}$”, Issledovaniya po Sovremennym Problemam Summirovaniya i Priblizheniya Funktsiy i ikh Prilozheniyam, DSU, Dnepropetrovsk, 1975, 66–68 (in Russian)

[11] V. F. Storchay, “Approximating the continuous functions of two variables by spline functions in metric $\mathbb{C}$”, Issledovaniya po Sovremennym Problemam Summirovaniya i Priblizheniya Funktsiy i ikh Prilozheniyam, DSU, Dnepropetrovsk, 1975, 82–89 (in Russian)

[12] V. N. Malozemov, “The deviation of polygonal functions”, Vestnik LSU, Series 1, 2:7 (1966), 150–153 (in Russian) | Zbl

[13] V. N. Malozemov, “Polygonal interpolation”, Math. Notes, 1:5 (1967), 355–357 | DOI | MR | MR | Zbl

[14] Sh. E. Mikeladze, Numerical Methods of Mathematical Analysis, Gostekhizdat, M., 1953 (in Russian) | MR