Optimal quadratures in the sense of Sard in a Hilbert space

Abdullo R. Hayotov, Gradimir V. Milovanović and Kholmat M. Shadimetov

Applied Mathematics and Computation, 2015, vol. 259, issue C, 637-653

Abstract: An optimal quadrature formula in the sense of Sard in the Hilbert space K2(Pm) is constructed. New optimal quadrature formula of such a type and explicit expressions for the corresponding optimal coefficients are obtained using S.L. Sobolev’s method. The obtained optimal quadrature formula is exact for the trigonometric functions sinωx,cosωx, and for algebraic polynomials of degree m-3. Finally, some numerical results for the norm of the error functional of the optimal quadrature formulas are presented.

Keywords: Optimal quadrature formulas; Error functional; Extremal function; Hilbert space; Optimal coefficients (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:637-653

DOI: 10.1016/j.amc.2015.02.093

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