Improved parameter selection strategy for the iterated Arnoldi-Tikhonov method
<|reference_start|>Improved parameter selection strategy for the iterated Arnoldi-Tikhonov method: 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.<|reference_end|>
@article{donatelli2024improved,
    title={Improved parameter selection strategy for the iterated Arnoldi-Tikhonov
  method},
    author={Marco Donatelli and Davide Furch`i},
    journal={arXiv preprint arXiv:2404.08321},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.08321},
    primaryClass={math.NA cs.NA}
}