FASTGL
Fast computation of Gauss-Legendre Quadrature Points and Weights

FASTGL is a FORTRAN90 library which carries out the fast computation of the K-th value and weight of an N-point Gauss-Legendre quadrature rule, by Ignace Bogaert.

Licensing:

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

Languages:

FASTGL is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LEGENDRE_RULE, a FORTRAN90 program which computes a Gauss-Legendre quadrature rule.

QUADMOM, a FORTRAN90 library 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).

QUADRULE, a FORTRAN90 library which contains information about quadrature rules, both as tabulated values, and as computational procedures.

TOMS655, a FORTRAN90 library which computes the weights for interpolatory quadrature rules; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky.

Reference:

1. Ignace Bogaert,
   Iteration-free computation of Gauss-Legendre quadrature nodes and weights,
   SIAM Journal on Scientific Computing,
   Volume 36, Number 3, 2014, pages A1008-1026.

Source Code:

• fastgl.f90, the source code.

Examples and Tests:

• fastgl_test.f90, a sample calling program.
• fastgl_test.txt, the output file.

List of Routines:

• BESSELJZERO computes the kth zero of the J0(X) Bessel function.
• BESSELJ1SQUARED computes the square of BesselJ(1, BesselZero(0,k))
• GLPAIR computes the k-th Gauss-Legendre pair of an N-point rule.
• GLPAIRS computes a node-weight pair, with k limited to half the range.
• GLPAIRTABULATED returns tabulated theta and weight values.
• LEGENDRE_THETA returns the K-th theta coordinate in an L point rule.
• LEGENDRE_WEIGHT returns the K-th weight in an L-point Legendre rule.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.