Runge Function
Runge's test function for interpolation techniques.
runge(x)
x |
numeric scalar. |
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.
Numerical value of the function.
## 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) }
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