On selection of the best coefficients in interpolatory quadrature rules

Abstract By using the least squares theory, an approach is employed to produce the best coefficients of interpolatory quadrature rules in L 2 space when the related nodes are already given. In this way, according to the concept of integration precision degree and moments of order k , a nonlinear system of equations is minimized and its solutions are then considered as the coefficients of new quadrature rules. Some examples are also given to clarify our approach.