Optimal Quadrature Formulas with Positive Coefficients in $L_2^{(m)}(0,1)$ Space

Kh. M. Shadimetov; A. R. Hayotov

Optimal Quadrature Formulas with Positive Coefficients in $L_2^{(m)}(0,1)$ Space

Numerical Analysis 2009-11-17 v1

Authors: Kh. M. Shadimetov , A. R. Hayotov

Abstract

In the Sobolev space $L_2^{(m)}(0,1)$ optimal quadrature formulas with the nodes (1.5) are investigated. For optimal coefficients explicit form are obtained and norm of the error functional is calculated. In particular, by choosing parameter $\eta_0$ in (1.5) the optimal quadrature formulas with positive coefficients are obtained and compared with well known optimal formulas.

Keywords

optimal quadrature formulas positive coefficients Sobolev space error functional numerical integration

Cite

@article{arxiv.0911.2896,
  title  = {Optimal Quadrature Formulas with Positive Coefficients in $L_2^{(m)}(0,1)$ Space},
  author = {Kh. M. Shadimetov and A. R. Hayotov},
  journal= {arXiv preprint arXiv:0911.2896},
  year   = {2009}
}

Comments

32 pages, submitted to the Journal of computational and applied mathematics

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