Revision 04bbc417cf2927b827660bc07743429783569aec authored by HwB on 10 February 2013, 00:00:00 UTC, committed by Gabor Csardi on 10 February 2013, 00:00:00 UTC
1 parent 0e3ae6b
eigjacobi.Rd
\name{eigjacobi}
\alias{eigjacobi}
\title{
Jacobi Eigenvalue Method
}
\description{
Jacobi's iteration method for eigenvalues and eigenvectors.
}
\usage{
eigjacobi(A, tol = .Machine$double.eps^(2/3))
}
\arguments{
\item{A}{a real symmetric matrix.}
\item{tol}{requested tolerance.}
}
\details{
The Jacobi eigenvalue method repeatedly performs (Givens) transformations
until the matrix becomes almost diagonal.
}
\value{
Returns a list with components \code{V}, a matrix containing the
eigenvectors as columns, and \code{D} a vector of the eigenvalues.
}
\note{
This R implementation works well up to 50x50-matrices.
}
\references{
Mathews, J. H., and K. D. Fink (2004). Numerical Methods Using Matlab.
Fourth edition, Pearson education, Inc., New Jersey.
}
\seealso{
\code{\link{eig}}
}
\examples{
A <- matrix(c( 1.06, -0.73, 0.77, -0.67,
-0.73, 2.64, 1.04, 0.72,
0.77, 1.04, 3.93, -2.14,
-0.67, 0.72, -2.14, 2.04), 4, 4, byrow = TRUE)
eigjacobi(A)
# $V
# [,1] [,2] [,3] [,4]
# [1,] 0.87019414 -0.3151209 0.1975473 -0.3231656
# [2,] 0.11138094 0.8661855 0.1178032 -0.4726938
# [3,] 0.07043799 0.1683401 0.8273261 0.5312548
# [4,] 0.47475776 0.3494040 -0.5124734 0.6244140
#
# $D
# [1] 0.66335457 3.39813189 5.58753257 0.02098098
}
\keyword{ math }
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