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.

翻译：迭代Arnoldi-Tikhonov（iAT）方法是一种正则化技术，特别适用于求解大规模不适定线性逆问题。通过将离散化问题投影到低维Krylov子空间并在该子空间中求解，该方法有效降低了计算复杂度。本文在离散化算子的附加假设条件下对iAT方法进行了研究。文中对近似误差进行了理论分析，由此推导出一种正则化参数的后验选取规则。与arXiv:2311.11823中最新提出的后验规则相比，我们提出的规则能够获得更精确的数值近似解。数值实验结果验证了理论分析的正确性，即使在新假设条件不满足的情况下，该方法仍能提供精确的计算解。