https://github.com/cran/pracma
Revision 26e049d70b4a1c237987e260cba68f6a9413736c authored by Hans W. Borchers on 09 April 2019, 04:10:07 UTC, committed by cran-robot on 09 April 2019, 04:10:07 UTC
1 parent bf07673
Tip revision: 26e049d70b4a1c237987e260cba68f6a9413736c authored by Hans W. Borchers on 09 April 2019, 04:10:07 UTC
version 2.2.5
version 2.2.5
Tip revision: 26e049d
halley.Rd
\name{halley}
\alias{halley}
\title{
Halley's Root Finding Mathod
}
\description{
Finding roots of univariate functions using the Halley method.
}
\usage{
halley(fun, x0, maxiter = 500, tol = 1e-08, ...)
}
\arguments{
\item{fun}{function whose root is to be found.}
\item{x0}{starting value for the iteration.}
\item{maxiter}{maximum number of iterations.}
\item{tol}{absolute tolerance; default \code{eps^(1/2)}}
\item{...}{additional arguments to be passed to the function.}
}
\details{
Well known root finding algorithms for real, univariate, continuous
functions; the second derivative must be smooth, i.e. continuous.
The first and second derivative are computed numerically.
}
\value{
Return a list with components \code{root}, \code{f.root},
the function value at the found root, \code{iter}, the number of iterations
done, and the estimated precision \code{estim.prec}
}
\references{
\url{http://mathworld.wolfram.com/HalleysMethod.html}
}
\seealso{
\code{\link{newtonRaphson}}
}
\examples{
halley(sin, 3.0) # 3.14159265358979 in the 3 iterations
halley(function(x) x*exp(x) - 1, 1.0)
# 0.567143290409784 Gauss' omega constant
# Legendre polynomial of degree 5
lp5 <- c(63, 0, -70, 0, 15, 0)/8
f <- function(x) polyval(lp5, x)
halley(f, 1.0) # 0.906179845938664
}
\keyword{ math }
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