Geodesic
The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 3, pp. 121-129 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S. M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in $L_P \ (1 \le p \infty)$ is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown.
Mots-clés : quadrature formula, gradient, node.
Keywords: curvilinear integral, error 
@article{MAIS_2013_20_3_a8,
     author = {K. Tukhliev},
     title = {The {Optimal} {Quadrature} {Formula} of {Approximate} {Calculation} of {Curvilinear} {Integral} of {First} {Kind} for {Some} {Classes} of {Functions} and {Curves}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {121--129},
     year = {2013},
     volume = {20},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_3_a8/}
}
TY  - JOUR
AU  - K. Tukhliev
TI  - The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2013
SP  - 121
EP  - 129
VL  - 20
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MAIS_2013_20_3_a8/
LA  - ru
ID  - MAIS_2013_20_3_a8
ER  - 
%0 Journal Article
%A K. Tukhliev
%T The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
%J Modelirovanie i analiz informacionnyh sistem
%D 2013
%P 121-129
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/MAIS_2013_20_3_a8/
%G ru
%F MAIS_2013_20_3_a8
K. Tukhliev. The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 3, pp. 121-129. http://geodesic.mathdoc.fr/item/MAIS_2013_20_3_a8/

[1] S. M. Nikolsky, Kvadraturnye formuly, Nauka, M., 1988 (in Russian) | MR

[2] M. Sh. Shabozov, F. M. Mirpochchoev, “Optimizatsiya priblizhennogo integrirovaniya krivolineynogo integrala pervogo roda dlya nekotorykh klassov funktsy i krivykh”, DAN RT, 53:6 (2010), 415–419 (in Russian)

[3] M. Sh. Shabozov, K. Tukhliev, “Optimalnye formuly priblizhennogo vychisleniya krivolineynogo integrala pervogo roda dlya nekotorykh klassov funktsiy i krivykh”, Sovremennye problemy matematicheskogo analiza i teorii funktsy, Materialy mezhdunarodnoy nauchnoy konferentsii (Dushanbe, 29–30 iyunya 2012 g.), Donish, Dushanbe, 2012, 197–206 (in Russian)

[4] M. B. Aksen, A. Kh. Turetsky, “O nailuchshikh kvadraturnykh formulakh dlya nekotorykh klassov funktsy”, DAN SSSR, 166:5 (1966), 1019–1021 (in Russian) | MR | Zbl