https://github.com/cran/pracma
Tip revision: 71455748623ef69836470c75c5f9384f6e872d45 authored by HwB on 28 June 2011, 00:00:00 UTC
version 0.6-3
version 0.6-3
Tip revision: 7145574
romberg.Rd
\name{romberg}
\alias{romberg}
\title{
Romberg Integration
}
\description{
Romberg Integration
}
\usage{
romberg(f, a, b, tol = .Machine$double.eps^(2/3), ...)
}
\arguments{
\item{f}{function to be integrated.}
\item{a, b}{end points of the interval.}
\item{tol}{requested tolerance.}
\item{...}{variables to be passed to the function.}
}
\details{
Simple Romberg integration with an explicit Richardson method applied
to a series of trapezoidal integrals.
}
\value{
List of value and relative error.
}
\references{
Mathews, J. H., and K. D. Fink (1999). Numerical Methods Using Matlab.
Third Edition, Prentice Hall.
}
\author{
HwB email: <hwborchers@googlemail.com>
}
\note{
The function does \emph{not} need to be vectorized.
The relative error can sometimes be scaringly high. It may help
to interchange the integration limits.
}
\seealso{
\code{\link{gauss_kronrod}}
}
\examples{
romberg(sin, 0, pi) # 2.000000000000001 , rel.error: 6.6e-13
romberg(exp, 0, 1) # 1.718281828459044 , rel.error: 3.6e-13
# 1.718281828459045 , i.e. exp(1) - 1
}
\keyword{ math }