On stable numerical differentiation

TL;DR

This paper introduces two numerical differentiation methods based on regularized Volterra equations, demonstrating their efficiency and competitiveness against variational regularization in handling noisy data.

Contribution

It presents two novel approaches for stable numerical differentiation using regularized Volterra equations, with comparative analysis and numerical experiments.

Findings

Methods are efficient for noisy data

Competitively outperform variational regularization

Numerical experiments validate effectiveness

Abstract

Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete favorably with the variational regularization method for stable calculating the derivatives of noisy functions.