Abstract
The construction of optimal interpolation formulas is discussed. First, an exact upper bound for the error of an interpolation formula in the Sobolev space is calculated. The existence and uniqueness are proved for the optimal interpolation formula with the smallest error. An algorithm for finding the coefficients of the optimal interpolation formula is presented. This algorithm makes it possible to find the optimal coefficients.
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Translated by V. Arutyunyan
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Shadimetov, K.M., Mamatova, N.H. On the Optimal Interpolation of Functions. Russ Math. 67, 53–63 (2023). https://doi.org/10.3103/S1066369X23120071
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DOI: https://doi.org/10.3103/S1066369X23120071