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.

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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 $W_2^n(\mathbb R)$. 
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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/

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