R: Gaussian Quadrature with Richardson Extrapolation

quadgr {pracma} | R Documentation

## Gaussian Quadrature with Richardson Extrapolation

### Description

Gaussian 12-point quadrature with Richardson extrapolation.

### Usage

    quadgr(f, a, b, tol = .Machine$double.eps^(1/2), ...)

### 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

`quadgr` uses a 12-point Gauss-Legendre quadrature. The error estimate is based on successive interval bisection. Richardson extrapolation accelerates the convergence for some integrals, especially integrals with endpoint singularities.

Through some preprocessing infinite intervals can also be handled.

### Value

List with `value` and `rel.err`.

### Author(s)

Copyright (c) 2009 Jonas Lundgren for the Matlab function `quadgr` available on MatlabCentral under the BSD license.

R re-implementation by HwB, email: <hwborchers@googlemail.com>, in 2011.

### See Also

`gaussLegendre`

### Examples

    ##  Dilogarithm function
    flog <- function(t) log(1-t)/t
    quadgr(flog, 1, 0, tol = 1e-12)
    # value
    # 1.6449340668482 , is pi^2/6 = 1.64493406684823
    # rel.err
    # 2.07167616395054e-13

[Package pracma version 2.0.4 Index]