QUADRATURE_RULES_CCN
Nested Clenshaw Curtis Rules

QUADRATURE_RULES_CCN 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.

Licensing:

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

Related Data and Programs:

CCN_RULE is a MATLAB program which defines a nested Clenshaw Curtis quadrature rule.

Sample Files:

CCN_D1_ORDER01, the nested Clenshaw Curtis rule of order 1.

• ccn_d1_order01_x.txt, the abscissas.
• ccn_d1_order01_w.txt, the weights.
• ccn_d1_order01_r.txt, the range.

CCN_D1_ORDER02, the nested Clenshaw Curtis rule of order 2.

• ccn_d1_order02_x.txt, the abscissas.
• ccn_d1_order02_w.txt, the weights.
• ccn_d1_order02_r.txt, the range.

CCN_D1_ORDER03, the nested Clenshaw Curtis rule of order 3.

• ccn_d1_order03_x.txt, the abscissas.
• ccn_d1_order03_w.txt, the weights.
• ccn_d1_order03_r.txt, the range.

CCN_D1_ORDER04, the nested Clenshaw Curtis rule of order 4.

• ccn_d1_order04_x.txt, the abscissas.
• ccn_d1_order04_w.txt, the weights.
• ccn_d1_order04_r.txt, the range.

CCN_D1_ORDER05, the nested Clenshaw Curtis rule of order 5.

• ccn_d1_order05_x.txt, the abscissas.
• ccn_d1_order05_w.txt, the weights.
• ccn_d1_order05_r.txt, the range.

CCN_D1_ORDER06, the nested Clenshaw Curtis rule of order 6.

• ccn_d1_order06_x.txt, the abscissas.
• ccn_d1_order06_w.txt, the weights.
• ccn_d1_order06_r.txt, the range.

CCN_D1_ORDER07, the nested Clenshaw Curtis rule of order 7.

• ccn_d1_order07_x.txt, the abscissas.
• ccn_d1_order07_w.txt, the weights.
• ccn_d1_order07_r.txt, the range.

CCN_D1_ORDER08, the nested Clenshaw Curtis rule of order 8.

• ccn_d1_order08_x.txt, the abscissas.
• ccn_d1_order08_w.txt, the weights.
• ccn_d1_order08_r.txt, the range.

CCN_D1_ORDER09, the nested Clenshaw Curtis rule of order 9.

• ccn_d1_order09_x.txt, the abscissas.
• ccn_d1_order09_w.txt, the weights.
• ccn_d1_order09_r.txt, the range.

CCN_D1_ORDER10, the nested Clenshaw Curtis rule of order 10.

• ccn_d1_order10_x.txt, the abscissas.
• ccn_d1_order10_w.txt, the weights.
• ccn_d1_order10_r.txt, the range.

CCN_D2_LEVEL00, sparse grid for dimension 2 and level 0, formed from the nested Clenshaw Curtis rule, using 1 point.

• ccn_d2_level00_x.txt, the abscissas.
• ccn_d2_level00_w.txt, the weights.
• ccn_d2_level00_r.txt, the range.
• ccn_d2_level00.png, a PNG image.

CCN_D2_LEVEL01, sparse grid for dimension 2 and level 1, formed from the nested Clenshaw Curtis rule, using 5 points.

• ccn_d2_level01_x.txt, the abscissas.
• ccn_d2_level01_w.txt, the weights.
• ccn_d2_level01_r.txt, the range.
• ccn_d2_level01.png, a PNG image.

CCN_D2_LEVEL02, sparse grid for dimension 2 and level 2, formed from the nested Clenshaw Curtis rule, using 13 points.

• ccn_d2_level02_x.txt, the abscissas.
• ccn_d2_level02_w.txt, the weights.
• ccn_d2_level02_r.txt, the range.
• ccn_d2_level02.png, a PNG image.

CCN_D2_LEVEL03, sparse grid for dimension 2 and level 3, formed from the nested Clenshaw Curtis rule, using 25 points.

• ccn_d2_level03_x.txt, the abscissas.
• ccn_d2_level03_w.txt, the weights.
• ccn_d2_level03_r.txt, the range.
• ccn_d2_level03.png, a PNG image.

CCN_D2_LEVEL04, sparse grid for dimension 2 and level 4, formed from the nested Clenshaw Curtis rule, using 41 points.

• ccn_d2_level04_x.txt, the abscissas.
• ccn_d2_level04_w.txt, the weights.
• ccn_d2_level04_r.txt, the range.
• ccn_d2_level04.png, a PNG image.

CCN_D2_LEVEL05, sparse grid for dimension 2 and level 5, formed from the nested Clenshaw Curtis rule, using 61 points.

• ccn_d2_level05_x.txt, the abscissas.
• ccn_d2_level05_w.txt, the weights.
• ccn_d2_level05_r.txt, the range.
• ccn_d2_level05.png, a PNG image.

CCN_D2_LEVEL06, sparse grid for dimension 2 and level 6, formed from the nested Clenshaw Curtis rule, using 85 points.

• ccn_d2_level06_x.txt, the abscissas.
• ccn_d2_level06_w.txt, the weights.
• ccn_d2_level06_r.txt, the range.
• ccn_d2_level06.png, a PNG image.

CCN_D2_LEVEL07, sparse grid for dimension 2 and level 7, formed from the nested Clenshaw Curtis rule, using 113 points.

• ccn_d2_level07_x.txt, the abscissas.
• ccn_d2_level07_w.txt, the weights.
• ccn_d2_level07_r.txt, the range.
• ccn_d2_level07.png, a PNG image.

CCN_D2_LEVEL08, sparse grid for dimension 2 and level 8, formed from the nested Clenshaw Curtis rule, using 145 points.

• ccn_d2_level08_x.txt, the abscissas.
• ccn_d2_level08_w.txt, the weights.
• ccn_d2_level08_r.txt, the range.
• ccn_d2_level08.png, a PNG image.

CCN_D2_LEVEL09, sparse grid for dimension 2 and level 9, formed from the nested Clenshaw Curtis rule, using 181 points.

• ccn_d2_level09_x.txt, the abscissas.
• ccn_d2_level09_w.txt, the weights.
• ccn_d2_level09_r.txt, the range.
• ccn_d2_level09.png, a PNG image.

CCN_D2_LEVEL10, sparse grid for dimension 2 and level 10, formed from the nested Clenshaw Curtis rule, using 221 points.

• ccn_d2_level10_x.txt, the abscissas.
• ccn_d2_level10_w.txt, the weights.
• ccn_d2_level10_r.txt, the range.
• ccn_d2_level10.png, a PNG image.

You can go up one level to the DATASETS page.