d1.poly: 1-dimensional Chebychev approximation

In squipbar/cheby: Computes Chebychev approximations to 1- and 2-dimensional functions

Description

Standard Chebychev approximation of an arbitrary function.

Usage

d1.poly(fn, range, iOrder, iPts, fn.opts = NULL, fn.vals = NULL,
  grid = NULL, details = FALSE)

Arguments

fn	a function f(x) or f(x,β) for β a list of function parameters. If the latter, must be coded with second argument a list names opts, i.e. fn <- function( x, opts )
range	the range of the approximation.
iOrder	the order of the polynomial approximation.
iPts	the number of points at which the approximation is computed. Must be at least as large as iOrder.
fn.opts	(optional) options passed to fn
fn.vals	the values of fn on grid. Useful if fn is very slow to evaluate.
grid	(optional) the grid on which the function is to be approximated.
details	If TRUE, returns extra details about the approximation.

Value

A function which approximates the input fn over the interval range. If details=TRUE, return is a list with entries fn, poly, fn.deriv, poly.deriv, residuals, which are, respectively, the approximating function, the polynomial desciption over [-1,1], the derivative of the approximation, the polynomial desciption of the derivative, and the approximation errors.

See Also

sp1.poly

Examples

cube <- function( x, opts ) opts$A * x^3
approx <- d1.poly( cube, c(-4,2), 4, 20, fn.opts=list(A=2) )
sapply( c(-3, -2, 0, .5 ), function( x ) abs( approx(x) - 2 * x ^ 3 ) )

squipbar/cheby documentation built on May 30, 2019, 8 a.m.