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| 1 | +\name{polintmat} |
| 2 | +\alias{polintmat} |
| 3 | +\title{ |
| 4 | +Polynomial extrapolation for a converging sequence of one or more values} |
| 5 | +\description{ |
| 6 | +For each value in a set \code{xa}, estimates the converged value. The process |
| 7 | +is called Richardson extrapolation. It terminates when all of two successive |
| 8 | +estimates are within a tolerance of each other. |
| 9 | +} |
| 10 | +\usage{ |
| 11 | +polintmat(xa, ya, x) |
| 12 | +} |
| 13 | +\arguments{ |
| 14 | + \item{xa}{Vector of length equal to the maximum number of iterations.} |
| 15 | + \item{ya}{Array with first dimension number of rows equal to length of \code{xa}, |
| 16 | + second dimension length equal number of basis functions, and |
| 17 | + third dimension of length 1.} |
| 18 | + \item{x}{A scalar value which, in our applications, is always zero.} |
| 19 | +} |
| 20 | +\details{ |
| 21 | +This function is called with in functions \code{monfn}, \code{mongrad} and |
| 22 | +\code{monhess}. This function computes the estimate for a single iteration |
| 23 | +of the convergence iterations. |
| 24 | +} |
| 25 | +\value{ |
| 26 | +A un-named list of length two containing these objects: |
| 27 | + \item{y:}{Matrix of order number of argument values by number of basis |
| 28 | + functions.} |
| 29 | + \item{dy:}{Array with same dimensions as argument \code{ya}.} |
| 30 | +} |
| 31 | +\references{ |
| 32 | + Ramsay, James O., Hooker, G. and Graves, S. (2009), \emph{Functional |
| 33 | + Data Analysis with R and Matlab}, Springer, New York. |
| 34 | + |
| 35 | + Ramsay, James O., and Silverman, |
| 36 | + Bernard W. (2005), \emph{Functional |
| 37 | + Data Analysis, 2nd ed.}, Springer, New York. |
| 38 | + |
| 39 | + Ramsay, James O., and Silverman, |
| 40 | + Bernard W. (2002), \emph{Applied |
| 41 | + Functional Data Analysis}, Springer, New York. |
| 42 | +} |
| 43 | +\author{ |
| 44 | + J. O. Ramsay |
| 45 | +} |
| 46 | +\seealso{ |
| 47 | + \code{\link{monfn}}, |
| 48 | + \code{\link{mongrad}}, |
| 49 | + \code{\link{monhess}} |
| 50 | +} |
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