ccn_rule


ccn_rule, a MATLAB code which generates a Clenshaw Curtis Nested (CCN) quadrature rule, based on a nested set of points inspired by the Clenshaw Curtis quadrature rule.

The data defining the rule is written to three files for easy use as input to other programs.

The Clenshaw Curtis Nested quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x) dx
      
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))
      

If the order of the CCN rule is 1, 3, 5, 9, 17, 33, or in general 2^L+1, then the rule is identical to the Clenshaw Curtis rule.

Otherwise, the rule is based on a subset of the points in the Clenshaw Curtis rule of next highest order in the sequence 2^L+1.

The CCN rule has no special accuracy properties, except that the rules of odd order are symmetric, and hence get one extra degree of precision. Moreover, the rules of even order have a single unpaired point which is assigned weight zero, so that it is equivalent to the immediately preceding rule of odd order.

Usage:

ccn_rule ( n, a, b, 'filename' )
where

Licensing:

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

Languages:

ccn_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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ccn_rule_test

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quadrature_rules_ccn, a dataset directory which contains quadrature rules for integration on [-1,+1], using a nested clenshaw curtis rule.

truncated_normal_rule, a MATLAB code which computes a quadrature rule for a normal probability density function (pdf), also called a gaussian distribution, that has been truncated to [a,+oo), (-oo,b] or [a,b].

Reference:

  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  3. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:


Last revised on 11 December 2018.