Clenshaw-Curtis Quadrature Formula
Clenshaw-Curtis Quadrature Formula
clenshaw_curtis(f, a = -1, b = 1, n = 1024, ...)
f |
function, the integrand, without singularities. |
a, b |
lower and upper limit of the integral; must be finite. |
n |
Number of Chebyshev nodes to account for. |
... |
Additional parameters to be passed to the function |
Clenshaw-Curtis quadrature is based on sampling the integrand on Chebyshev points, an operation that can be implemented using the Fast Fourier Transform.
Numerical scalar, the value of the integral.
Trefethen, L. N. (2008). Is Gauss Quadrature Better Than Clenshaw-Curtis? SIAM Review, Vol. 50, No. 1, pp 67–87.
## Quadrature with Chebyshev nodes and weights f <- function(x) sin(x+cos(10*exp(x))/3) ## Not run: ezplot(f, -1, 1, fill = TRUE) cc <- clenshaw_curtis(f, n = 64) #=> 0.0325036517151 , true error > 1.3e-10
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