On determination of optimal coefficients of a quadrature formula of Hermite type in the Sobolev space W˜2(m) (T1)

Numerous publications are devoted to quadrature formulas; they include the values of derivatives of integrable functions. When, besides the values of function f at points x on T1, the values of its derivatives of some orders are also known, then naturally, with the correct use of all these data, a m...

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Bibliographic Details
Published in:AIP conference proceedings 2024-03, Vol.3004 (1)
Main Authors: Rustamov, Hakim, Jalolov, Islomjon, Isomiddinov, Bekzodjon
Format: Article
Language:English
Subjects:
Derivatives
Functionals
Quadratures
Sobolev space
Upper bounds
Online Access:Get full text
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Summary:Numerous publications are devoted to quadrature formulas; they include the values of derivatives of integrable functions. When, besides the values of function f at points x on T1, the values of its derivatives of some orders are also known, then naturally, with the correct use of all these data, a more accurate result can be expected than in the case of using only the values of the functions. For the error functional of the quadrature formula of Hermite type for functions of class W˜2(m) (T1), the norms are found; an upper bound is obtained, and the optimal coefficients of the quadrature formula of Hermite type are determined for p (x) = 1 and m = 4 (α = 0, 1, 2, 3).
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0199865