swh:1:snp:1d6f9c912933e835b749aef1f8077112982fe84e
Tip revision: 85eeff77b2e878cc9dbd7659e4acbc035be93c28 authored by Hans W. Borchers on 22 September 2022, 13:50:02 UTC
version 2.4.2
version 2.4.2
Tip revision: 85eeff7
laguerre.Rd
\name{laguerre}
\alias{laguerre}
\title{
Laguerre's Method
}
\description{
Laguerre's method for finding roots of complex polynomials.
}
\usage{
laguerre(p, x0, nmax = 25, tol = .Machine$double.eps^(1/2))
}
\arguments{
\item{p}{real or complex vector representing a polynomial.}
\item{x0}{real or complex point near the root.}
\item{nmax}{maximum number of iterations.}
\item{tol}{absolute tolerance.}
}
\details{
Uses values of the polynomial and its first and second derivative.
}
\value{
The root found, or a warning about the number of iterations.
}
\references{
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab.
Second edition, Prentice Hall.
}
\note{
Computations are caried out in complex arithmetic, and it is possible
to obtain a complex root even if the starting estimate is real.
}
\seealso{
\code{\link{roots}}
}
\examples{
# 1 x^5 - 5.4 x^4 + 14.45 x^3 - 32.292 x^2 + 47.25 x - 26.46
p <- c(1.0, -5.4, 14.45, -32.292, 47.25, -26.46)
laguerre(p, 1) #=> 1.2
laguerre(p, 2) #=> 2.099987 (should be 2.1)
laguerre(p, 2i) #=> 0+2.236068i (+- 2.2361i, i.e sqrt(-5))
}
\keyword{ math }