Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$

2016 ◽  
Vol 74 (2) ◽  
pp. 307-336 ◽  
Author(s):  
N. D. Boltaev ◽  
A. R. Hayotov ◽  
Kh. M. Shadimetov
Keyword(s):  
Sobolev Space ◽  
Fourier Coefficients ◽  
Quadrature Formulas ◽  
Optimal Quadrature ◽  
Optimal Quadrature Formulas

An optimal quadrature formula in the Sobolev space

2021 ◽  
Vol 65 (3) ◽  
pp. 46-59
Keyword(s):  
Sobolev Space ◽  
Quadrature Formula ◽  
Approximate Calculation ◽  
Order Of Convergence ◽  
Quadrature Formulas ◽  
Explicit Formulas ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature ◽  
Optimal Coefficients ◽  
Optimal Quadrature Formulas

This paper studies the problem of construction of optimal quadrature formulas for approximate calculation of integrals with trigonometric weight in the L(2m)(0, 1) space for any ω ൐= 0, ω ∈ R. Here explicit formulas for the optimal coefficients are obtained. We study the order of convergence of the optimal formulas for the case m = 1, 2. The obtained optimal quadrature formulas are exact for Pm−1(x), where Pm−1(x) is a polynomial of degree (m − 1).

scholarly journals OPTIMAL QUADRATURE FORMULAS FOR FOURIER COEFFICIENTS IN W2(m,m-1) 2 SPACE

2017 ◽  
Vol 7 (4) ◽  
pp. 1233-1266
Author(s):  
Nurali D. Boltaev ◽  
◽  
Abdullo R. Hayotov ◽  
Kholmat M. Shadimetov ◽  
Keyword(s):  
Fourier Coefficients ◽  
Quadrature Formulas ◽  
Optimal Quadrature ◽  
Optimal Quadrature Formulas

Optimal quadrature formulas with derivatives in the Sobolev space

2018 ◽  
Vol 2018 (3) ◽  
pp. 18-28
Author(s):  
D.M. Akhmedov ◽  
N.H. Mamatova ◽  
F.A. Nuraliyev
Keyword(s):  
Sobolev Space ◽  
Quadrature Formulas ◽  
Optimal Quadrature ◽  
Optimal Quadrature Formulas
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