 Some methods utilize formulas to approximate the weights and then use a few iterations of Newton-Raphson to lower the error of the approximation to below machine precision .In 1969, Golub and Welsch published their method for computing Gaussian quadrature rules given the three term recurrence relation that the underlying orthogonal polynomials satisfy.They reduce the problem of computing the nodes of a Gaussian quadrature rule to the problem of finding the eigenvalues of a particular symmetric tridiagonal matrix.