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易处理性的概念。对于此类算子方程，基于噪声水平的最佳可能重构率的渐近性质在许多情形下是已知的。然而，相关问题是：为达到该最佳可能精度，需要何种由噪声水平驱动的离散化程度？所提出的概念借鉴了信息复杂性理论。若干实例表明，该概念在应对维数灾难方面具有相关性。