A novel methodology for measured data fitting

This paper presents a novel methodology for data fitting using a piecewise rational function. That function is able to satisfy any regularity conditions through the direct setting of some free parameters. Moreover, in any grid point of a defined grid we can impose simultaneous interpolation conditions of both the samples and their derivatives. The value of the interpolation function in any point of the input domain depends only on the closest four grid points in its neighborhood. This property bounds the uncertainty propagation in the case of noisy data. A suitable procedure permits to extend the grid beyond the convex hull, so keeping the described properties of the interpolation without affecting the function in the other regions