TY  - INPR
A1  - Blanchard, Gilles
A1  - Mathé, Peter
T1  - Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
N2  - The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 7 
Y1  - 2012
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/5553
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-57117
ER  -