2024/01/18 by Peter Mathé, Mathé, Peter, Bernd Hofmann +1
Computer Science · Engineering · Mathematics · #65D15 #68Q27 #FOS: Mathematics #Image and Signal Denoising Methods #Non-Destructive Testing Techniques #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2401.09919
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.