Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab

In this paper, we investigate variants of the well-known Golub and Welsch algorithm for computing nodes and weights of Gaussian quadrature rules for symmetric weights w in intervals (−a, a) (not necessarily bounded). The purpose is to reduce the complexity of the Jacobi eigenvalue problem stemming from Wilf’s theorem and show the effectiveness of Matlab implementations of our variants for reducing the computer times compared to some other methods. Numerical examples on three test problems show the benefits of these variants.