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：我们针对Hilbert空间中的不适定算子方程引入了一种可解性概念。对于此类算子方程，在给定噪声水平下最优重建速率的新近性已在多数情形下为已知。然而关键问题在于：为达到该最优精度，所需的离散化程度（同样受噪声水平驱动）应如何界定。所提出的概念借鉴了信息复杂度理论。若干实例表明，该概念在应对维度灾难时具有重要价值。