gl_fast_rule

gl_fast_rule, 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 information on this web page is distributed under the MIT license.

Languages:

gl_fast_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

gl_fast_rule_test

matlab_rule, a MATLAB code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

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.