quadrule_fast, 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.


The computer code and data files made available on this web page are distributed under the MIT license


quadrule_fast is available in a MATLAB version.

Related Data and Programs:

clenshaw_curtis_rule, a MATLAB code which can compute Clenshaw Curtis rules for 1 dimensional or multidimensional problems.

product_rule, a MATLAB code which can create a multidimensional quadrature rule as a product of one dimensional rules.

quadrule, a MATLAB code which contains quadrature rules.


stroud, a MATLAB code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.


  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:

Last revised on 25 February 2019.