Quadrature Points and Weights, Golub Welsch Method

QUADRATURE_GOLUB_WELSCH is a FORTRAN77 library which illustrates the use of the Golub Welsch technique for computing the points and weights of a Gaussian quadrature rule.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


QUADRATURE_GOLUB_WELSCH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CLENSHAW_CURTIS_RULE, a FORTRAN77 program which defines a Clenshaw Curtis quadrature rule.

QUADRATURE_LEAST_SQUARES, a FORTRAN77 library 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.

QUADRATURE_WEIGHTS_VANDERMONDE, a FORTRAN77 library which determines the weights of a quadrature rule using the Vandermonde matrix.

QUADRULE, a FORTRAN77 library which defines quadrature rules for 1-dimensional domains.

TOMS655, a FORTRAN77 library which computes the weights for interpolatory quadrature rule;
this library is commonly called IQPACK;
this is a FORTRAN90 version of ACM TOMS algorithm 655.


  1. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  2. Sylvan Elhay, Jaroslav Kautsky,
    Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
    ACM Transactions on Mathematical Software,
    Volume 13, Number 4, December 1987, pages 399-415.
  3. Jaroslav Kautsky, Sylvan Elhay,
    Calculation of the Weights of Interpolatory Quadratures,
    Numerische Mathematik,
    Volume 40, 1982, pages 407-422.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 21 February 2014.