Discrete analogs of Taikov’s inequality and recovery of sequences given with an error
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We consider the problem of the recovery of the kth order divided difference from a sequence given with an errorwith bounded divided difference of nth order, 0 ≤ k < n. The solution of this problem involves an extremal problem similar to that known in the continuous case as Taikov’s inequality.
Keywordsrecovery of sequences given with an error Taikov’s inequality kth order divided difference implicit-function theorem Sobolev class W2n (ℝ)
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