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
lebesgue.Rd
\name{lebesgue}
\alias{lebesgue}
\title{Lebesgue Constant}
\description{
Estimates the Lebesgue constant.
}
\usage{
lebesgue(x, refine = 4, plotting = FALSE)
}
\arguments{
\item{x}{numeric vector of grid points}
\item{refine}{refine the grid with \code{2^refine} grid points;
can only be an integer between 2 and 10, default 4.}
\item{plotting}{shall the Lebesgue function be plotted.}
}
\details{
The Lebesgue constant gives an estimation \eqn{||P_n f|| \le L ||f||}
(in minimax norm) where \eqn{P_n f} is the interpolating polynomial of
order \eqn{n} for \eqn{f} on an interval \eqn{[a, b]}.
}
\value{
Lebesgue constant for the given grid points.
}
\references{
Berrut, J.-P., and L. Nick Trefethen (2004). ``Barycentric Lagrange
Interpolation''. SIAM Review, Vol. 46(3), pp.501--517.
}
\note{
The Lebesgue constant plays an important role when estimating the distance
of interpolating polynomials from the minimax solution (see the Remez
algorithm).
}
\seealso{
\code{\link{barylag}}
}
\examples{
lebesgue(seq(0, 1, length.out = 6)) #=> 3.100425
}
\keyword{ math }
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