LibLip - Matlab toolbox for multivariate scattered data approximation

Uses Lipschitz properties of a function to interpolate or approximate it from scattered data.

LibLip provides many methods to interpolate scattered data (with or without preprocessing) by using only the data itself and one additional parameter -- the Lipschitz constant (which is basically the upper bound on the slope of the function). The Lipschitz constant can be automatically estimated from the data.
LibLip also provides approximation methods using locally Lipschitz functions.

If the data contains noise, it can be smoothened using special techniques which rely on linear programming. Lipschitz constant can also be estimated from noisy data by using sample splitting and cross-validation.

In addition LibLip also accommodates monotonicity and range constraints. It is useful for approximation of functions that are known to be monotone with respect to all or a subset of variables, as well as monotone only on parts of the domain. Range constraints accommodate non-constant bounds on the values of the data and the interpolant.