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On the problem of optimal interpolation of functions

Kh. M. ShadimetovTashkent State Transport University; V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of SciencesN. H. MamatovaBukhara State University; V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Izvestiya Vysshikh Uchebnykh Zavedenii Matematikajournal2023en
ABI

Abstract

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.

Topics

Advanced Numerical Analysis TechniquesMathematical functions and polynomialsAdvanced Computational Techniques in Science and Engineering

Identifiers

DOI
10.26907/0021-3446-2023-12-59-70

Citations and references

Cited by 37 references
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