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In the present paper using S.L. Sobolev’s method interpolation splines minimizing the semi-norm in a Hilbert space are constructed. Explicit formulas for coefficients of interpolation splines are obtained. The obtained interpolation spline is exact for polynomials of degree m?2 and e ?x . Also some numerical results are presented. 相似文献
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This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the \(L_{2}^{(m)}(0,1)\) 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+1≥m, 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 \(L_{2}^{(m)}(0,1)\) space are exact for P m?1(x), where P m?1(x) is a polynomial of degree m?1. Furthermore, we present some numerical results, which confirm the obtained theoretical results. 相似文献
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Nurali Boltaev Abdullo Hayotov Gradimir Milovanovi Kholmat Shadimetov 《Journal of Applied Analysis & Computation》2017,7(4):1233-1266
This paper studies the problem of construction of optimal
quadrature formulas in the sense of Sard in the
$W_2^{(m,m-1)}[0,1]$ space for calculating Fourier coefficients. Using S.~L.\ Sobolev''s method we
obtain new optimal quadrature formulas of such type for $N 1\geq
m$, where $N 1$ is the number of the nodes. Moreover, explicit
formulas for the optimal coefficients are obtained. We investigate
the order of convergence of the optimal formula for $m=1$. The obtained optimal quadrature formula in the
$W_2^{(m,m-1)}[0,1]$ space is exact for $\exp(-x)$ and
$P_{m-2}(x)$, where $P_{m-2}(x)$ is a polynomial of degree $m-2$.
Furthermore, we present some numerical results, which confirm the obtained theoretical results. 相似文献
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Abdullo Rakhmonovich Hayotov Gradimir V. Milovanović Kholmat Mahkambaevich Shadimetov 《Numerical Algorithms》2011,57(4):487-510
In this paper we construct an optimal quadrature formula in the sense of Sard in the Hilbert space K
2(P
2). Using S.L. 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 L2(2)(0,1)L_2^{(2)}(0,1). The obtained optimal quadrature formula is exact for the trigonometric functions sinx and cosx. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula. 相似文献
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