| 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 |
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