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.

翻译：Arnoldi-Tikhonov方法是一种成熟的用于求解大规模不适定线性逆问题的正则化技术。该方法利用Arnoldi分解将离散化问题投影到低维Krylov子空间中进行求解，从而降低计算复杂度。本文对迭代Arnoldi-Tikhonov方法进行了深入研究，开展了涵盖所有近似误差的全面分析。此外，本文提出了一种选择正则化参数的新策略，与标准Arnoldi-Tikhonov方法相比，该策略能够获得更精确的近似解。数值结果进一步证实，所提方法对正则化参数具有鲁棒性。