R: Adaptive Gauss-Kronrod Quadrature

quadgk {pracma} | R Documentation

## Adaptive Gauss-Kronrod Quadrature

### Description

Adaptive Gauss-Kronrod Quadrature.

### Usage

    quadgk(f, a, b, tol = .Machine$double.eps^0.5, ...)

### Arguments

`f` | integrand as function, may have singularities at the endpoints.
`a, b` | endpoints of the integration interval.
`tol` | relative tolerence.
`...` | Additional parameters to be passed to the function `f`.

### Details

Adaptive version of the (7, 15)-point Gauss-Kronrod quadrature formula, where in each recursion the error is taken as the difference between these two estimated integrals.

### Value

Value of the integration. The relative error should be of the same order of magnitude as the relative tolerance (or much smaller).

### Note

Uses the same nodes and weights as the `quadQK15` procedure in the QUADPACK library.

### See Also

`gauss_kronrod`

### Examples

    ##  Dilogarithm function
    flog <- function(t) log(1-t)/t
    quadgk(flog, 1, 0, tol = 1e-12)
    # 1.644934066848128 - pi^2/6 < 1e-13

[Package pracma version 2.0.4 Index]