Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method
Abstract
The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the discretized problem into a lower-dimensional Krylov subspace, in which it is solved. This paper explores the iterated Arnoldi-Tikhonov method, conducting a comprehensive analysis that addresses all approximation errors. Additionally, it introduces a novel strategy for choosing the regularization parameter, leading to more accurate approximate solutions compared to the standard Arnoldi-Tikhonov method. Moreover, the proposed method demonstrates robustness with respect to the regularization parameter, as confirmed by the numerical results.
Cite
@article{arxiv.2311.11823,
title = {Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method},
author = {Davide Bianchi and Marco Donatelli and Davide Furchì and Lothar Reichel},
journal= {arXiv preprint arXiv:2311.11823},
year = {2025}
}