Abstract:
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, $0\le k<n$. 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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