Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$
| Autor: | Nurali D. Boltaev, Kh.M. Shadimetov, Abdullo R. Hayotov |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Applied Mathematics Numerical analysis Mathematical analysis Hilbert space 010103 numerical & computational mathematics 01 natural sciences Quadrature (mathematics) 010101 applied mathematics Sobolev space symbols.namesake Rate of convergence Theory of computation symbols 0101 mathematics Fourier series Mathematics |
| Zdroj: | Numerical Algorithms. 74:307-336 |
| ISSN: | 1572-9265 1017-1398 |
| DOI: | 10.1007/s11075-016-0150-7 |
| Popis: | This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the L2(m)(0,1)$L_{2}^{(m)}(0,1)$ space for numerical calculation of Fourier coefficients. Using the S.L.Sobolev's method, we obtain new optimal quadrature formulas of such type for N+1źm, where N+1 is the number of nodes. Moreover, explicit formulas for the optimal coefficients are obtained. We study the order of convergence of the optimal formula for the case m=1. The obtained optimal quadrature formulas in the L2(m)(0,1)$L_{2}^{(m)}(0,1)$ space are exact for Pmź1(x), where Pmź1(x) is a polynomial of degree mź1. Furthermore, we present some numerical results, which confirm the obtained theoretical results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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