On stable numerical differentiation
This work addresses the problem of stable numerical differentiation for noisy data, offering alternative methods that perform comparably to existing variational regularization.
The paper proposes two approaches for stable numerical differentiation based on a regularized Volterra equation, demonstrating through experiments that they are efficient and competitive with variational regularization methods for computing derivatives of noisy functions.
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.