R: Gauss-Kronrod Quadrature

gauss_kronrod {pracma} | R Documentation

## Gauss-Kronrod Quadrature

### Description

Simple Gaussian-Kronrod quadrature formula.

### Usage

    gauss_kronrod(f, a, b, ...)

### Arguments

`f` | function to be integrated.
`a, b` | end points of the interval.
`...` | variables to be passed to the function.

### Details

Gaussian quadrature of degree 7 with Gauss-Kronrod of degree 15 for error estimation, the `quadQK15` procedure in the QUADPACK library.

### Value

List of value and relative error.

### Note

The function needs to be vectorized (though this could easily be changed), but the function does not need to be defined at the end points.

### References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

### See Also

`quadgk`, `romberg`

### Examples

    gauss_kronrod(sin, 0, pi)  #  2.000000000000000 , rel.error: 1.14e-12
    gauss_kronrod(exp, 0, 1)   #  1.718281828459045 , rel.error: 0
                               #  1.718281828459045 , i.e. exp(1) - 1

[Package pracma version 2.0.4 Index]