CCN_RULE is a MATLAB program 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) dxis 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.
ccn_rule ( n, a, b, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
CCN_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
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CCN_09 is a nested Clenshaw Curtis rule of order 9, which will exactly match the standard Clenshaw Curtis rule.
ccn_rule ( 9, -1, +1, 'ccn_o9' )
ccn_rule ( 9, -1, +1, 'ccn_o9' )
ccn_rule ( 9, -1, +1, 'ccn_o9' )
You can go up one level to the MATLAB source codes.