Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space
arXiv:0810.54218 citationsh-index: 20
Originality Synthesis-oriented
AI Analysis
For researchers in numerical integration, this is an incremental extension of Sobolev's method to a specific function space.
This paper constructs optimal quadrature formulas in the $W_2^{(m,m-1)}(0,1)$ space using Sobolev's algorithm, deriving optimal coefficients for m=1 and m=2. No concrete numerical results are provided.
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 $$ \int\limits_0^1ϕ(x)dx\cong \sum\limits_{β=0}^NC_βϕ(x_β). $$