QUADRATURE_RULES_CHEBYSHEV1 is a dataset directory which contains some examples of quadrature rules of Gauss-Chebyshev type 1.
The Gauss-Chebyshev type 1 quadrature rule is designed to approximate integrals on the interval [-1,1], with a weight function of the form 1/sqrt (1-x^2).
Gauss-Chebyshev type 1 quadrature assumes that the integrand we are considering has a form like:
Integral ( -1 <= x <= +1 ) f(x) / sqrt(1-x^2) dx
The standard Gauss-Chebyshev type 1 quadrature rule is used as follows:
Integral ( -1 <= x <= +1 ) f(x) / sqrt(1-x^2) dxis to be approximated by
Sum ( 1 <= i <= order ) 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 endpoints of the region.
We consider a Gauss-Chebyshev type 1 quadrature rule of order 4.
Here is the text of the "W" file storing the weights of such a rule:
0.7853981633974483
0.7853981633974483
0.7853981633974483
0.7853981633974483
Here is the text of the "X" file storing the abscissas of such a rule:
-0.9238795325112867
-0.3826834323650898
0.3826834323650897
0.9238795325112867
Here is the text of the "R" file storing the lower and upper limits of the region:
-1.0
+1.0
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
CHEBYSHEV1_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
INT_EXACTNESS_CHEBYSHEV1, a FORTRAN90 program which reads files defining a Gauss-Chebyshev type 1 quadrature rule, and test it for exactness against monomial integrands.
TEST_INT, a C++ library which defines test integrands for 1D quadrature rules.
Gauss-Chebyshev Type 1 Rule, Order 1.
Gauss-Chebyshev Type 1 Rule, Order 2.
Gauss-Chebyshev Type 1 Rule, Order 4.
Gauss-Chebyshev Type 1 Rule, Order 8.
Gauss-Chebyshev Type 1 Rule, Order 16.
Gauss-Chebyshev Type 1 Rule, Order 32.
You can go up one level to the DATASETS page.