Work

Fast numerical derivatives of univariate functions on non-uniform grids

Year: 2025

Type: article

Abstract: 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.

Source: Journal of Computational and Applied Mathematics

DOI: 10.1016/j.cam.2025.116619

Authors: Nadaniela Egidi, Josephin Giacomini, Pierluigi Maponi

Institution: Università di Camerino

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, Faculty of Science and Engineering, University of Manchester