Geodesic
On the problem of optimal interpolation of functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 59-70

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In this work, the problem of constructing optimal interpolation formulas is discussed. Here, first, an exact upper bound for the error of the interpolation formula in the Sobolev space is calculated. The existence and uniqueness of the optimal interpolation formula, which gives the smallest error, are proved. An algorithm for finding the coefficients of the optimal interpolation formula is given. By implementing this algorithm, the optimal coefficients are found.
Keywords: Sobolev space, extremal function, composite lattice optimal cubature formulas, error functional. 
@article{IVM_2023_12_a4,
     author = {Kh. M. Shadimetov and N. H. Mamatova},
     title = {On the problem of optimal interpolation of functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {59--70},
     publisher = {mathdoc},
     number = {12},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_12_a4/}
}
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Kh. M. Shadimetov; N. H. Mamatova. On the problem of optimal interpolation of functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 59-70. http://geodesic.mathdoc.fr/item/IVM_2023_12_a4/