Numerical derivation of multivariate functions

We consider the problem of the numerical derivation of a function of several real variables. The proposed numerical method is based on the singular value expansion of the integral formulation of the derivative problem generalised to the multivariate case. The resulting derivation method is able to compute the partial derivatives of a multivariate function sampled at points in general position. The accuracy of the proposed method is analysed and confirmed by numerical tests performed for different distributions of the sampling points.