Optimal quadratures in the sense of Sard in a Hilbert space

Abdullo R Hayotov,Gradimir V Milovanović,Kholmat M Shadimetov

doi:10.1016/j.amc.2015.02.093

Optimal quadratures in the sense of Sard in a Hilbert space

Abdullo R Hayotov, Gradimir V Milovanović + Show 1 more

https://doi.org/10.1016/j.amc.2015.02.093

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Journal: Applied Mathematics and Computation	Publication Date: Mar 25, 2015
Citations: 24

Affiliation: National University of Uzbekistan, Serbian Academy of Sciences and Arts, State University of Novi Pazar

#Optimal Quadrature Formula #Sense Of Sard + Show 8 more

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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.

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