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

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.

arXiv comment32 pages, submitted to the Journal of computational and applied mathematics