Runge Function

Runge's test function for interpolation techniques.

runge(x)

Arguments

x

numeric scalar.

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.

Value

Numerical value of the function.

See also

fnorm

Examples

if (FALSE) { # \dontrun{
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) }
} # }