In the present article, the problem of constructing the optimal quadrature formula in the sense of Sard is discussed for numerical integration of the weighted integrals in the Hilbert space of real-valued functions. Initially, the norm of the error functional is found using the extremal function of the error functional of the quadrature formula. Since the error functional is defined on the Hilbert space, the quadrature formula that we are constructing is exact for zeros of this space, that is, we have the conditions that the influence of the error functional on these functions is equal to zero. Then, the Lagrange function is constructed to find the conditional extremum of the error functional norm. Thereby, a system of linear equations is obtained for the coefficients of the optimal quadrature formula.
| Mualliflar | Babaev, S.S., Бабаев, С.С. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 99-107 |
| Til | Ingliz |
quadrature formula with derivatives, extremal function, error functional, optimal coefficient, Lagrange function, квадратурная формула с производными, экстремальная функция, функционал погрешности, оптимальный коэффициент, функция Лагранжа
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