Gaussian Quadrature with Richardson Extrapolation
Gaussian 12-point quadrature with Richardson extrapolation.
quadgr(f, a, b, tol = .Machine$double.eps^(1/2), ...)
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 |
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.
List with value and rel.err.
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.
gaussLegendre
## 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
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