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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 517, Pages 12–21
DOI: https://doi.org/10.31857/S2686954324030026 (Mi danma523) 		 
MATHEMATICS

Bernstein–Riemann interpolation formula for arbitrary continuous functions on an interval

A. N. Agadzhanov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954324030026
Abstract: For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.
Keywords: interpolation, local Bernstein polynomials, binomial coefficients, Euler gamma functions, multiplicative Gauss formula, Riemann zeta function, Riemann type functions, Weierstrass type functions, Besicovich type functions, Takagi type functions.
Presented: S. N. Vassilyev
Received: 13.09.2023
Revised: 10.04.2024
Accepted: 26.04.2024
English version:
Doklady Mathematics, 2024, Volume 109, Issue 3, Pages 197–205
DOI: https://doi.org/10.1134/S1064562424702028
Bibliographic databases:
Document Type: Article
UDC: 519.652+517.589
Language: Russian
Citation: A. N. Agadzhanov, “Bernstein–Riemann interpolation formula for arbitrary continuous functions on an interval”, Dokl. RAN. Math. Inf. Proc. Upr., 517 (2024), 12–21; Dokl. Math., 109:3 (2024), 197–205
Citation in format AMSBIB
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\by A.~N.~Agadzhanov
\paper Bernstein--Riemann interpolation formula for arbitrary continuous functions on an interval
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 517
\pages 12--21
\mathnet{http://mi.mathnet.ru/danma523}
\crossref{https://doi.org/10.31857/S2686954324030026}
\elib{https://elibrary.ru/item.asp?id=69204682}
\transl
\jour Dokl. Math.
\yr 2024
\vol 109
\issue 3
\pages 197--205
\crossref{https://doi.org/10.1134/S1064562424702028}
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