Gaussian quadrature weights and nodes


Here we present, a number of files/routines to enable the user to easily compute Gaussian quadrature weights and abscissas. You can just open the link and copy-and-paste the text into your system.
  1. GQpoints.m---This is a simple MATLAB m-file function which sets the values of the weights and abscissas for n = 2, 4, 8, 16, or 32.

2. gaussxw.m---This is a MATLAB m-file taken from Trefethen's paper, "Is Gauss quadrature better than Clenshaw-Curtis?" SIAM Rev. 50 (2008), no. 1, 67–87, which computes the weights and abscissas for any value of n, by solving a tridiagonal eigenvalue problem. (See the paper for the details.)

3. gauss64.dat, gauss128.dat, gauss256.dat, gauss512.dat---These are ASCII text files with the abscissas and then the weights arranged as a single vector of length 2N, where N = 64, 128, 256, or 512. If you click on the hot link the file is opened and you can easily copy-and-paste the values into a file on your system, which you can then save using the MATLAB save command and read using the load command. The abscissas occupy the first N positions in the vector, and the weights occupy the last N positions. Eventually I hope to add a file containing the N = 1024 values.