  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.
