Geodesic
On efficient approximation of piecewise smooth functions with their presentation by rapidly converging piecewise polynomial series
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 1, pp. 67-77 
V. V. Smelov. On efficient approximation of piecewise smooth functions with their presentation by rapidly converging piecewise polynomial series. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 1, pp. 67-77. http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a5/
@article{SJVM_2004_7_1_a5,
     author = {V. V. Smelov},
     title = {On efficient approximation of piecewise smooth functions with their presentation by rapidly converging piecewise polynomial series},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {67--77},
     year = {2004},
     volume = {7},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a5/}
}
TY  - JOUR
AU  - V. V. Smelov
TI  - On efficient approximation of piecewise smooth functions with their presentation by rapidly converging piecewise polynomial series
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2004
SP  - 67
EP  - 77
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a5/
LA  - ru
ID  - SJVM_2004_7_1_a5
ER  - 
%0 Journal Article
%A V. V. Smelov
%T On efficient approximation of piecewise smooth functions with their presentation by rapidly converging piecewise polynomial series
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2004
%P 67-77
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a5/
%G ru
%F SJVM_2004_7_1_a5

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

A variant of expansion of piecewise smooth functions in rapidly converging series about specific piecewise polynomial functions is proposed. These specific functions are constructed on the basis of the Legendre polynomials. This paper is the sequel of the author's previous publications [1] and forms the basis of the efficient approximations of the above-mentioned functions.

[1] Smelov V. V., Zadachi Shturma–Liuvillya i razlozheniya funktsii v bystro-skhodyaschiesya ryady, Izd-vo SO RAN, Novosibirsk, 2000

[2] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976 | MR

[3] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967 | MR

[4] Marchuk G. I., Metody rascheta yadernykh reaktorov, Gosatomizdat, M., 1961

[5] Babuška I., Craid A., Mandel J., Pitkaranta J., Efficient preconditioning for the $p$-version finite element method in two dimensions, Institute for Phys. Sci. and Technology University of Maryland and Depart. of Math. University of Colorado at Denver, 1989

[6] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[7] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR

[8] Vladimirov B. C., Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits, Tr. matematicheskogo instituta imeni V. A. Steklova, 61, Moskva, 1961, 3–158

[9] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 2, GITTL, M.-L., 1948

[10] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR | Zbl