R: Runge Function

runge {pracma} | R Documentation

## Runge Function

### Description

Runge's test function for interpolation techniques.

### Usage

    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

    ## 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)

[Package pracma version 2.0.4 Index]