runge: Runge Function

Description

Runge's test function for interpolation techniques.

Usage

runge(x)

Arguments

numeric scalar.

Value

Numerical value of the function.

Details

Runge's function is a classical test function for interpolation and and approximation techniques, especially for equidistant nodes.

For example, when approximating the Runge function on the interval [-1, 1], the error at the endpoints will diverge when the number of nodes is increasing.

Examples

Run this code

## Not run: 
# x <- seq(-1, 1, length.out = 101)
# y <- runge(x)
# plot(x, y, type = "l", lwd = 2, col = "navy", ylim = c(-0.2, 1.2))
# grid()
# 
# n <- c(6, 11, 16)
# for (i in seq(along=n)) {
#     xp <- seq(-1, 1, length.out = n[i])
#     yp <- runge(xp)
#     p  <- polyfit(xp, yp, n[i]-1)
#     y  <- polyval(p, x)
#     lines(x, y, lty=i) }
# ## End(Not run)