pracma (version 1.8.8)

barylag: Barycentric Lagrange Interpolation

Description

Barycentric Lagrange interpolation in one dimension.

Usage

barylag(xi, yi, x)

Arguments

xi, yi

x- and y-coordinates of supporting nodes.

x

x-coordinates of interpolation points.

Value

• Values of interpolated data at points x.

Details

barylag interpolates the given data using the barycentric Lagrange interpolation formula (vectorized to remove all loops).

References

Berrut, J.-P., and L. Nick Trefethen (2004). ``Barycentric Lagrange Interpolation''. SIAM Review, Vol. 46(3), pp.501--517.

See Also

Lagrange or Newton interpolation.

Examples

##  Generates an example with plot.
# Input:
#   fun  ---  function that shall be 'approximated'
#   a, b ---  interval [a, b] to be used for the example
#   n    ---  number of supporting nodes
#   m    ---  number of interpolation points
# Output
#   plot of function, interpolation, and nodes
#   return value is NULL (invisible)
barycentricExample <- function(fun, a, b, n, m)
{
	xi <- seq(a, b, len=n)
	yi <- fun(xi)
	x  <- seq(a, b, len=m)

	y <- barylag(xi, yi, x)
	plot(xi, yi, col="red", xlab="x", ylab="y",
		main="Example of barycentric interpolation")

	lines(x, fun(x), col="yellow", lwd=2)
	lines(x, y, col="darkred")

	grid()
}

barycentricExample(sin, -pi, pi, 11, 101)  # good interpolation
barycentricExample(runge, -1, 1, 21, 101)  # bad interpolation