pracma (version 1.9.9)

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)
## Not run: 
# 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
# ## End(Not run)