Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space

Abstract

In this paper problem of construction of optimal quadrature formulas in $W_2^{(m,m-1)}(0,1)$ space is considered. Here by using Sobolev's algorithm when $m=1,2$ we find the optimal coefficients of the quadrature formulas of the form $$ \int\limits_0^1ϕ(x)dx\cong \sum\limits_{β=0}^NC_βϕ(x_β). $$