Optimal quadrature formulas with positive coefficients in L2(m) (0,1) space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Shadimetov, Kh M.¹  Hayotov, A. R.¹ 

[1] Uzbek Acad Sci, Inst Math & Informat Technol, Dept Computat Methods, Tashkent 700135, Uzbekistan

关键词: Sobolev space;    Optimal quadrature formula;    Positive coefficients;    Error functional;   

DOI  :  10.1016/j.cam.2010.07.021

来源: Elsevier

【 摘 要 】

In the Sobolev space L-2((m)) (0, 1) optimal quadrature formulas of the form integral(1)(0) phi(x)dx congruent to Sigma(beta=0) C-beta phi(x(beta)) with the nodes x(i) = eta(i)h, x(N-i) = 1 - eta(i)h, i = (0, t - 1) over bar, 0 <= eta(0) < eta(1) < ... < eta(t-1) < t, t is an element of N, x(beta) = h beta, t <= beta <= N - t, h = 1/N are investigated. For optimal coefficients C-beta explicit forms are obtained and the norm of the error functional is calculated for any natural numbers m and N. In particular, in the case t = 1 and eta(0) = 0.205 for m = 2, 3...., 14 optimal quadrature formulas with positive coefficients are numerically obtained and some of them are compared with well-known optimal formulas. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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