An FFT method for the numerical differentiation

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 numer-ical experiment conducted for comparing the proposed method performance with that of the Neville Algorithm implemented in the NAG library.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

This paper discusses the numerical differentiation of a function tabulated at equidistant points. The proposed method utilizes the Fast Fourier Transform (FFT) and the singular value expansion of a Volterra integral operator to reformulate the derivative operator. The convergence analysis of the proposed method is provided, and a numerical experiment is conducted to compare its performance with that of the Neville algorithm implemented in the NAG library.