Optimal quadrature formula in space

2012 ◽  
Vol 62 (12) ◽  
pp. 1893-1909 ◽  
Author(s):  
Kh.M. Shadimetov ◽  
A.R. Hayotov ◽  
S.S. Azamov
Keyword(s):  
Quadrature Formula ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature

scholarly journals Optimal quadrature formula in the sense of Sard in K2(P3) space

2014 ◽  
Vol 95 (109) ◽  
pp. 29-47 ◽  
Author(s):  
Abdullo Hayotov ◽  
Gradimir Milovanovic ◽  
Kholmat Shadimetov
Keyword(s):  
Hilbert Space ◽  
Sobolev Space ◽  
Quadrature Formula ◽  
Asymptotic Optimality ◽  
Trigonometric Functions ◽  
Numerical Examples ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature ◽  
Optimal Coefficients ◽  
Optimal Formula

We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using 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 L (3)2 (0, 1). The obtained optimal quadrature formula is exact for the trigonometric functions sin x, cos x and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

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).

On an optimal quadrature formula in the sense of Sard

2010 ◽  
Vol 57 (4) ◽  
pp. 487-510 ◽  
Author(s):  
Abdullo Rakhmonovich Hayotov ◽  
Gradimir V. Milovanović ◽  
Kholmat Mahkambaevich Shadimetov
Keyword(s):  
Quadrature Formula ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature
Sign in / Sign up

Export Citation Format

Share Document