\name{rcond}
\title{Estimate the Reciprocal Condition Number}
\usage{
rcond(x, type, \dots)
}
\alias{rcond}
% methods are documented in Matrix-class.Rd
\description{
Estimate the reciprocal of the condition number of a matrix.
This is a generic function with several methods, as seen by
\code{\link{showMethods}(rcond)}.
}
\arguments{
\item{x}{an \R object that inherits from the \code{Matrix} class.}
\item{type}{
Character indicating the type of norm to be used in the estimate.
The default is \code{"O"} for the 1-norm. The other possible value is
\code{"I"} for the infinity norm.
}
\item{\dots}{further arguments passed to or from other methods.}
}
\value{
An estimate of the reciprocal condition number of \code{x}.
}
\section{BACKGROUND}{
The condition number of a matrix is the product of the matrix and
the norm of its inverse (or pseudo-inverse if the matrix is not
square).
Since it can take on values between 1 and infinity, inclusive, it
can be viewed as a measure of how close a matrix is to being rank
deficient.
It can also be viewed as a factor by which errors in solving linear
systems with this matrix as coefficient matrix could be magnified.
Condition numbers are usually estimated, since exact computation is
costly in terms of floating-point operations.
An (over) estimate of reciprocal condition number is given, since by
doing so overflow is avoided.
Matrices are well-conditioned if the reciprocal condition number is
near 1 and ill-conditioned if it is near zero.
}
\references{
Golub, G., and Van Loan, C. F. (1989).
\emph{Matrix Computations,}
2nd edition, Johns Hopkins, Baltimore.
}
\examples{
x <- Matrix(rnorm(9), 3, 3)
rcond(x)
rcond(Hilbert(9)) # should be about 9.1e-13
}
\keyword{array}
\keyword{algebra}