Geodesic
Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 515-527

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

We consider the problem of the recovery of the $k$th order divided difference from a sequence given with an error with bounded divided difference of $n$th order, $0\le k$. The solution of this problem involves an extremal problem similar to that known in the continuous case as Taikov's inequality.
Keywords: recovery of sequences given with an error, Taikov's inequality, $k$th order divided difference, implicit-function theorem, Sobolev class $W_2^n(\mathbb R)$. 
@article{MZM_2012_92_4_a2,
     author = {E. V. Vvedenskaya and K. Yu. Osipenko},
     title = {Discrete {Analogs} of {Taikov's} {Inequality} and {Recovery} of {Sequences} {Given} with an {Error}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {515--527},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a2/}
}
TY  - JOUR
AU  - E. V. Vvedenskaya
AU  - K. Yu. Osipenko
TI  - Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error
JO  - Matematičeskie zametki
PY  - 2012
SP  - 515
EP  - 527
VL  - 92
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a2/
LA  - ru
ID  - MZM_2012_92_4_a2
ER  - 
%0 Journal Article
%A E. V. Vvedenskaya
%A K. Yu. Osipenko
%T Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error
%J Matematičeskie zametki
%D 2012
%P 515-527
%V 92
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a2/
%G ru
%F MZM_2012_92_4_a2
E. V. Vvedenskaya; K. Yu. Osipenko. Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 515-527. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a2/