https://github.com/cran/pracma
Tip revision: fdf16693b000f3e309c56091892c61f0ec9fd670 authored by Hans W. Borchers on 21 November 2017, 16:15:00 UTC
version 2.1.1
version 2.1.1
Tip revision: fdf1669
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 = 100, tol = .Machine$double.eps^0.5)
}
\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)}}
}
\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 }