The paper by Gene H. Golub and John H. Welsch presents algorithms for computing Gauss quadrature rules, which are used to approximate integrals by polynomial integration. The authors show that the quadrature rule can be generated by computing the eigenvalues and the first component of the orthonormalized eigenvectors of a symmetric tridiagonal matrix, given the three-term recurrence relation for the orthogonal polynomials generated by the weight function. Additionally, an algorithm is provided to compute the three-term recurrence relation from the moments of the weight function. The paper includes a detailed description of the computational procedures, including the use of the Q-R algorithm for eigenvalue computation, and compares the methods through a test program. The results are validated against tables for Gauss-Legendre and Gauss-Laguerre quadrature. The authors acknowledge Professor Walter Gautschi for his contributions to the development of the methods discussed.The paper by Gene H. Golub and John H. Welsch presents algorithms for computing Gauss quadrature rules, which are used to approximate integrals by polynomial integration. The authors show that the quadrature rule can be generated by computing the eigenvalues and the first component of the orthonormalized eigenvectors of a symmetric tridiagonal matrix, given the three-term recurrence relation for the orthogonal polynomials generated by the weight function. Additionally, an algorithm is provided to compute the three-term recurrence relation from the moments of the weight function. The paper includes a detailed description of the computational procedures, including the use of the Q-R algorithm for eigenvalue computation, and compares the methods through a test program. The results are validated against tables for Gauss-Legendre and Gauss-Laguerre quadrature. The authors acknowledge Professor Walter Gautschi for his contributions to the development of the methods discussed.