Year: 2024
Type: preprint
Abstract: The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the discretized problem into a lower-dimensional Krylov subspace, where the problem is then solved. This paper studies iAT under an additional hypothesis on the discretized operator. It presents a theoretical analysis of the approximation errors, leading to an a posteriori rule for choosing the regularization parameter. Our proposed rule results in more accurate computed approximate solutions compared to the a posteriori rule recently proposed in arXiv:2311.11823. The numerical results confirm the theoretical analysis, providing accurate computed solutions even when the new assumption is not satisfied.
Source: arXiv (Cornell University)
Authors: Donatelli, Marco, Furchì, Davide
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394838909