Chebyshev norm

Also called the norm, this is the L_p norm with . In the Chebyshev norm, the distance between two sets of points or two lines is just the largest distance between any pair of points or the separation between two lines at the point where they are the farthest apart. A Chebyshev approximation minimizes the maximum distance between the data and the approximating function, hence the occasional name minimax approximation.

The use of the Chebyshev norm is indicated in many cases where the residuals of the fit are known not to follow a Gaussian distribution, in particular for all approximations of an empirical nature, where residuals are dominated by the inadequacy of the approximation rather than the errors of the measurements being approximated.

Programs performing fits using the Chebyshev norm are usually more time consuming than least squares fit programs, but can be found in some program libraries. A specific application to track fitting can be found in James83.