Description Usage Arguments Details Value Note See Also Examples

The `fnorm`

function calculates several different types of function
norms for depending on the argument `p`

.

1 | ```
fnorm(f, g, x1, x2, p = 2, npoints = 100)
``` |

`f, g` |
functions given by name or string. |

`x1, x2` |
endpoints of the interval. |

`p` |
Numeric scalar or Inf, -Inf; default is 2. |

`npoints` |
number of points to be considered in the interval. |

`fnorm`

returns a scalar that gives some measure of the distance
of two functions `f`

and `g`

on the interval `[x1, x2]`

.

It takes `npoints`

equidistant points in the interval, computes the
function values for `f`

and `g`

and applies `Norm`

to
their difference.

Especially `p=Inf`

returns the maximum norm,
while `fnorm(f, g, x1, x2, p = 1, npoints) / npoints`

would return some estimate of the mean distance.

Numeric scalar (or `Inf`

), or `NA`

if one of these functions
returns `NA`

.

Another kind of ‘mean’ distance could be calculated by integrating the
difference `f-g`

and dividing through the length of the interval.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
xp <- seq(-1, 1, length.out = 6)
yp <- runge(xp)
p5 <- polyfit(xp, yp, 5)
f5 <- function(x) polyval(p5, x)
fnorm(runge, f5, -1, 1, p = Inf) #=> 0.4303246
fnorm(runge, f5, -1, 1, p = Inf, npoints = 1000) #=> 0.4326690
# Compute mean distance using fnorm:
fnorm(runge, f5, -1, 1, p = 1, 1000) / 1000 #=> 0.1094193
# Compute mean distance by integration:
fn <- function(x) abs(runge(x) - f5(x))
integrate(fn, -1, 1)$value / 2 #=> 0.1095285
``` |

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