quad_fast_rule

quad_fast_rule, a MATLAB code which implements fast and efficient forms of several popular quadrature rules.

The quadrature rules are defined on the interval [-1,1], and assume there is no additional weighting factor in the data.

The fast implementations are exhibited and discussed in the papers by Trefethen and Waldvogel.

Licensing:

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

Languages:

quad_fast_rule is available in a MATLAB version and an Octave version.

Related Data and Programs:

quad_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. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
2. Charles Clenshaw, Alan Curtis,
   A Method for Numerical Integration on an Automatic Computer,
   Numerische Mathematik,
   Volume 2, Number 1, December 1960, pages 197-205.
3. Lloyd Trefethen,
   Is Gauss Quadrature Better Than Clenshaw-Curtis?,
   SIAM Review,
   Volume 50, Number 1, 2008, pages 67-87.
4. Joerg Waldvogel,
   Fast Construction of the Fejer and Clenshaw-Curtis Quadrature Rules,
   BIT Numerical Mathematics,
   Volume 43, Number 1, 2003, pages 1-18.

Source Code:

• clenshaw_curtis_integrate.m applies a Clenshaw Curtis quadrature rule.
• clenshaw_curtis_integrate_fast.m applies a Clenshaw Curtis quadrature rule, using an efficient MATLAB implementation.
• clenshaw_curtis_rule_compute.m computes a Clenshaw Curtis quadrature rule.
• clenshaw_curtis_rule_set.m sets a Clenshaw Curtis quadrature rule by looking it up in a table.
• fejer1_integrate_fast.m applies a Fejer type 1 quadrature rule, using an efficient MATLAB implementation.
• fejer1_rule_compute.m computes a Fejer type 1 quadrature rule.
• fejer1_rule_set.m sets a Fejer type 1 quadrature rule by looking it up in a table.
• fejer2_integrate_fast.m applies a Fejer type 2 quadrature rule, using an efficient MATLAB implementation.
• fejer2_rule_compute.m computes a Fejer type 2 quadrature rule.
• fejer2_rule_set.m sets a Fejer type 2 quadrature rule by looking it up in a table.
• gauss_legendre_integrate_fast.m applies a Gauss-Legendre quadrature rule, using an efficient MATLAB implementation.
• gauss_legendre_rule_compute.m computes a Gauss Legendre quadrature rule.
• gauss_legendre_rule_set.m sets a Gauss Legendre quadrature rule by looking it up in a table.