quadmom, a FORTRAN90 code which computes a Gaussian quadrature rule for a weight function rho(x) based on the Golub-Welsch procedure that only requires knowledge of the moments of rho(x).
The standard Golub-Welsch procedure expects to work with the coefficients alpha() and beta() of the three term recursion for the orthogonal polynomials associated with the weight function rho(x).
However, in the same paper, Golub and Welsch discuss a related procedure which, to compute a Gaussian quadrature rule of order N, requires the values of the first M=2*N+1 moments associated with rho(x):
mu(k) = integral x^k rho(x) dx, 0 <= k <= 2*nThis library demonstrates this moment-based procedure.
Executing the sample program requires access to the TOMS655 library as well.
The computer code and data files made available on this web page are distributed under the MIT license
quadmom is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
QUADRATURE_GOLUB_WELSCH, a FORTRAN90 code which computes the points and weights of a Gaussian quadrature rule using the Golub-Welsch procedure, assuming that the points have been specified.
QUADRATURE_LEAST_SQUARES, a FORTRAN90 code which computes weights for "sub-interpolatory" quadrature rules, that is, it estimates integrals by integrating a polynomial that approximates the function data in a least squares sense.
QUADRULE, a FORTRAN90 code which contains information about quadrature rules, both as tabulated values, and as computational procedures.
TOMS655, a FORTRAN90 code which computes the weights for interpolatory quadrature rules; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky.