fastgl

fastgl, a MATLAB code 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 MIT 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:

fastgl_test

legendre_rule, a MATLAB code which computes a Gauss-Legendre quadrature rule.

quadmom, a MATLAB 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).

quadrule, a MATLAB code which contains information about quadrature rules, both as tabulated values, and as computational procedures.

toms655, a MATLAB code 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:

• besseljzero.m, computes the kth zero of the J0(X) Bessel function.
• besselj1squared.m, computes the square of BesselJ(1, BesselZero(0,k)).
• glpair.m, computes the k-th Gauss-Legendre pair of an N-point rule.
• glpairs.m, computes the k-th Gauss-Legendre pair of an N-point rule.
• glpairtabulated.m, computes the k-th Gauss-Legendre pair of an N-point rule.
• legendre_theta.m, returns the K-th theta coordinate in an L point rule.
• legendre_weight.m, returns the K-th weight in an L point rule.