\name{hessian}
\alias{hessian}
\title{
Hessian Matrix
}
\description{
Numerically compute the Hessian matrix.
}
\usage{
hessian(f, x0, h = 1e-4, ...)
}
\arguments{
\item{f}{univariate function of several variables.}
\item{x0}{point in \eqn{R^n}.}
\item{h}{step size.}
\item{...}{variables to be passed to \code{f}.}
}
\details{
Computes the hessian matrix based on the three-point central difference
formula, expanded to two variables.
Assumes that the function has continuous partial derivatives.
}
\value{
An n-by-n matrix with \eqn{\frac{\partial^2 f}{\partial x_i \partial x_j}}
as (i, j) entry.
}
\author{
HwB <hwborchers@googlemail.com>
}
\references{
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab.
Second edition, Prentice Hall.
}
\seealso{
\code{\link{fderiv}}, \code{\link{laplacian}}
}
\examples{
f <- function(x) cos(x[1] + x[2])
x0 <- c(0, 0)
hessian(f, x0)
f <- function(u) {
x <- u[1]; y <- u[2]; z <- u[3]
return(x^3 + y^2 + z^2 +12*x*y + 2*z)
}
x0 <- c(1,1,1)
hessian(f, x0)
}
\keyword{ math }