We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases. However, the relevant question is, which level of discretization, again driven by the noise level, is required in order to achieve this best possible accuracy. The proposed concept adapts the one from Information-based Complexity. Several examples indicate the relevance of this concept in the light of the curse of dimensionality.

翻译：我们引入了Hilbert空间中不适定算子方程的可处理性概念。对于此类算子方程，在许多情况下，基于底层噪声水平的最佳可能重建速率的渐近性是已知的。然而，相关的问题在于，为实现这一最佳精度，需要何种程度的离散化（同样由噪声水平驱动）。所提出的概念借鉴了基于信息的复杂性理论。几个示例表明，该概念在应对维数灾难时具有相关性。