# barylag: Barycentric Lagrange Interpolation In pracma: Practical Numerical Math Functions

 barylag R Documentation

## 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.

### Details

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

### Value

Values of interpolated data at points `x`.

### Note

Barycentric interpolation is preferred because of its numerical stability.

### References

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

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)
``````

pracma documentation built on Nov. 10, 2023, 1:14 a.m.