A New Approach to the Quadrature Rules with Gaussian Weights and Nodes

To compute integrals on bounded or unbounded intervals we propose a new numerical approach by using weights and nodes of the classical Gauss quadrature rules. An account of the error and the convergence theory is given for the proposed quadrature formulas which have the advantage of reducing the condition number of the linear system arising when applying Nystr¨om methods to solve integral equations. Numerical examples confirming the theoretical results are provided to illustrate the accuracy of the introduced method.