On selection of the best coefficients in interpolatory quadrature rules

By using the least squares theory, an approach is employed to produce the best coefficients of interpolatory quadrature rules in L2 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.