Optimal quadratures in the sense of Sard in a Hilbert space
| Autor: | Kholmat M. Shadimetov, Gradimir V. Milovanović, Abdullo R. Hayotov |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Quadrature domains Applied Mathematics Mathematical analysis Gauss–Laguerre quadrature Gauss–Kronrod quadrature formula Tanh-sinh quadrature Mathematics::Numerical Analysis Numerical integration Computational Mathematics Gauss–Jacobi quadrature Gauss–Hermite quadrature Mathematics Clenshaw–Curtis quadrature |
| Zdroj: | Applied Mathematics and Computation. 259:637-653 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2015.02.093 |
| Popis: | An optimal quadrature formula in the sense of Sard in the Hilbert space K 2 ( P m ) 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 sin ω x , cos ω x , 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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