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**2005**- (**download**) (**as text**) (**annotate**)*Wed Jul 18 14:46:20 2007 UTC*(12 years, 1 month ago) by*maechler*File size: 2237 byte(s)

norm() for sparse; systematic checking of norm() and all "Summary" methods

\name{rcond} \title{Estimate the Reciprocal Condition Number} \alias{rcond} % most methods are documented in <foo>Matrix-class.Rd \alias{rcond,ANY,missing-method} \alias{rcond,matrix,character-method} \alias{rcond,Matrix,character-method} \alias{rcond,ldenseMatrix,character-method} \alias{rcond,ndenseMatrix,character-method} % \usage{ rcond(x, type, \dots) } \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, see also \code{\link{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 \code{\link{norm}} of the matrix and the norm of its inverse (or pseudo-inverse). The condition number takes on values between 1 and infinity, inclusive, and can be viewed as a factor by which errors in solving linear systems with this matrix as coefficient matrix could be magnified. \code{rcond()} computes the \emph{reciprocal} condition number with values in \eqn{[0,1]} and can be viewed as a scaled measure of how close a matrix is to being rank deficient (aka \dQuote{singular}). 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. } \seealso{ \code{\link{norm}}, \code{\link[base]{solve}}. } \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}

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