| Autor: |
Hohage, Thorsten, Weidling, Frederic |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
SIAM J. Numer. Anal. 55, 598-620, 2017 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1137/16M1067445 |
| Popis: |
We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of ill-posedness of the forward operator in terms of a family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. If the forward operator can be written in terms of the functional calculus of a Laplace-Beltrami operator, variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems. |
| Databáze: |
arXiv |
| Externí odkaz: |
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