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arXiv · 2311.11823

Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method

Davide Bianchi·Marco Donatelli·Davide Furchì·Lothar Reichel
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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.

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Davide Bianchi, Marco Donatelli, Davide Furchì, Lothar Reichel. 2023-11-20. Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method. https://doi.org/10.1007/s00211-025-01472-9

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