Optimal quadrature formula in the sense of Sard in K2(P3) space

Autor:	Kholmat M. Shadimetov, Gradimir V. Milovanović, Abdullo R. Hayotov
Rok vydání:	2014
Předmět:	Quadrature domains General Mathematics Mathematical analysis Gauss–Laguerre quadrature Gauss–Jacobi quadrature Applied mathematics Gauss–Kronrod quadrature formula Tanh-sinh quadrature Gauss–Hermite quadrature Clenshaw–Curtis quadrature Quadrature (mathematics) Mathematics
Zdroj:	Publications de l'Institut Math?matique (Belgrade). 95:29-47
ISSN:	1820-7405 0350-1302
DOI:	10.2298/pim1409029h
Popis:	We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using Sobolev?s method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space L (3)2 (0, 1). The obtained optimal quadrature formula is exact for the trigonometric functions sin x, cos x and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::000eea9eb88f0eb7f7adff09181844a8 https://doi.org/10.2298/pim1409029h Zobrazit plný text záznamu Plný text ve formátu PDF