R: Clenshaw-Curtis Quadrature Formula

clenshaw_curtis {pracma} | R Documentation

## Clenshaw-Curtis Quadrature Formula

### Description

Clenshaw-Curtis Quadrature Formula

### Usage

    clenshaw_curtis(f, a = -1, b = 1, n = 1024, ...)

### Arguments

`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

### Details

Clenshaw-Curtis quadrature is based on sampling the integrand on Chebyshev points, an operation that can be implemented using the Fast Fourier Transform.

### Value

Numerical scalar, the value of the integral.

### References

Trefethen, L. N. (2008). Is Gauss Quadrature Better Than Clenshaw-Curtis? SIAM Review, Vol. 50, No. 1, pp 67–87.

### See Also

`gaussLegendre`, `gauss_kronrod`

### Examples

    ##  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

[Package pracma version 2.0.4 Index]