Geodesic
The module function approximation by Bernstein polynomials
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 6-40

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

We obtain all the basic formulas connected with the approximation of $f(x)=|2x-1|$ by Bernstein polynomials. The estimates of the maximal coefficients in the polynomials are given. Degree of approximation for different points $x\in[0,1]$ is investigated. It is shown that near the point $x=1/2$ acceptable degree of approximation achieved on polynomials which are not computable from a practical point of view.
Keywords: the module function approximation, Bernstein polynomials. 
@article{VCHGU_2012_15_a1,
     author = {I. V. Tikhonov and V. B. Sherstyukov},
     title = {The module function approximation by {Bernstein} polynomials},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {6--40},
     publisher = {mathdoc},
     number = {15},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a1/}
}
TY  - JOUR
AU  - I. V. Tikhonov
AU  - V. B. Sherstyukov
TI  - The module function approximation by Bernstein polynomials
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2012
SP  - 6
EP  - 40
IS  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a1/
LA  - ru
ID  - VCHGU_2012_15_a1
ER  - 
%0 Journal Article
%A I. V. Tikhonov
%A V. B. Sherstyukov
%T The module function approximation by Bernstein polynomials
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2012
%P 6-40
%N 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a1/
%G ru
%F VCHGU_2012_15_a1
I. V. Tikhonov; V. B. Sherstyukov. The module function approximation by Bernstein polynomials. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 6-40. http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a1/