Year: 2025
Type: article
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.
Source: Numerische Mathematik
Authors: Davide Bianchi, Marco Donatelli, Davide Furchí, Lothar Reichel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4410465670