An FFT method for the numerical differentiation.

• Use of the FFT for fast numerical derivative computation. • Use of the SVE of the integral kernel associated to derivative operator of a generic order. • Proof of the order of convergence of the proposed method. • Development of a robust algorithm for first order derivative. • Generalization of the algorithm to higher order derivatives. • Generalization of the algorithm to derivatives of multivariate functions. We consider the numerical differentiation of a function tabulated at equidistant points. The proposed method is based on the Fast Fourier Transform (FFT) and the singular value expansion of a proper Volterra integral operator that reformulates the derivative operator. We provide the convergence analysis of the proposed method and the results of a numerical experiment conducted for comparing the proposed method performance with that of the Neville Algorithm implemented in the NAG library. [ABSTRACT FROM AUTHOR]