Fast numerical derivatives of univariate functions on non-uniform grids

An algorithm for computing the derivative of a function, starting from its values at randomly chosen points is presented. This algorithm uses the singular value expansion of the derivative operator and the discrete Fourier transformations. The convergence of the numerical discretization scheme is analyzed in a simplified case, while the order of convergence and the stability are evaluated by numerical simulations. • A new spectral method for the numerical derivatives of a function sampled at scattered points. • Proof of convergence of the proposed method in a simplified version. • A fast algorithm exploiting fast Discrete Fourier transformations. • Preliminary stability tests including noisy data.