\name{bisect}
\alias{bisect}
\alias{regulaFalsi}
\title{
Rootfinding through Bisection
}
\description{
Finding roots of univariate functions in bounded intervals.
}
\usage{
bisect(f, a, b, maxiter = 100, tol = .Machine$double.eps^0.5)
regulaFalsi(f, a, b, maxiter = 100, tol = .Machine$double.eps^0.5)
}
\arguments{
\item{f}{Function or its name as a string.}
\item{a, b}{interval end points.}
\item{maxiter}{maximum number of iterations; default 100.}
\item{tol}{absolute tolerance; default \code{eps^(1/2)}}
}
\details{
Well known root finding algorithms for real, univariate, continuous
functions. Bisection works in any case iff the function has opposite
signs at the endpoints of the interval.
``Regula falsi'' combines bisection and secant methods. The so-called
`Illinois' improvement is used.
}
\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 \code{root}, and the estimated accuracy \code{estim.prec}
}
\references{
Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics.
Second Edition, Springer-Verlag, Berlin Heidelberg.
}
\author{
Hans W Borchers <hwborchers@googlemail.com>
}
\seealso{
\code{\link{uniroot}}
}
\examples{
# Legendre polynomial of degree 5
lp5 <- c(63, 0, -70, 0, 15, 0)/8
f <- function(x) polyval(lp5, x)
bisect(f, 0.6, 1) # 0.9061798453 correct to 9 decimals
regulaFalsi(f, 0.6, 1) # 0.9061798459 correct to 10 decimals
}
\keyword{ math }