QUADRATURE_RULES_CLENSHAW_CURTIS is a dataset directory which contains examples of Clenshaw Curtis quadrature rules for the interval [-1,+1]. A quadrature rule is a set of n points x and associated weights w so that the integral of a function f(x) over some particular region can be approximated by:
Integral f(x) dx = Sum ( 1 <= i <= n ) w(i) * f(x(i))
For this directory, a quadrature rule is stored as three files, containing the weights, the points, and a file containing two points defining the corners of the rectangular region. The dimension of the region is deduced implicitly from the dimension of the points.
Here are the files for a Clenshaw Curtis rule of order 9:
Here is the text of an "W" file storing the weights of such a rule
0.1587301587301588E-01 0.1462186492160182 0.2793650793650794 0.3617178587204897 0.3936507936507936 0.3617178587204898 0.2793650793650794 0.1462186492160182 0.1587301587301588E-01
Here is the text of a "X" file storing the abscissas of such a rule:
-1.0000000000000000 -0.9238795325112867 -0.7071067811865475 -0.3826834323650897 0.000000000000000 0.3826834323650898 0.7071067811865475 0.9238795325112867 1.0000000000000000
Here is the text of an "R" file storing the lower and upper limits of the region, needed to determine the integration region:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.
SANDIA_RULES, a C++ library which produces 1D quadrature rules of Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, Legendre and Patterson types.
SPARSE_GRID_CC, a dataset directory which contains multidimensional Smolyak sparse grids based on the 1D Clenshaw Curtis rule;
TOMS424, a FORTRAN77 library which estimates the integral of a function using Clenshaw-Curtis quadrature.
CC_O1, Clenshaw Curtis rule of order 1:
CC_O2, Clenshaw Curtis rule of order 2:
CC_O3, Clenshaw Curtis rule of order 3:
CC_O4, Clenshaw Curtis rule of order 4:
CC_O5, Clenshaw Curtis rule of order 5:
CC_O9, Clenshaw Curtis rule of order 9:
CC_O17, Clenshaw Curtis rule of order 17:
CC_O33, Clenshaw Curtis rule of order 33:
CC_O65, Clenshaw Curtis rule of order 65:
You can go up one level to the DATASETS page.