Volume 41, pp. 81-92, 2014.

On convergence rates for quasi-solutions of ill-posed problems

Andreas Neubauer and Ronny Ramlau

Abstract

Usually, one needs information about the noise level to find proper regularized solutions when solving ill-posed problems. However, for several inverse problems, it is not easy to obtain an accurate estimation of the noise level. If one has information about bounds of the solution in some stronger norm, quasi-solutions are an excellent alternative. Besides existence, stability, and convergence results, it is the major emphasis of this paper to prove convergence rates for quasi-solutions in Hilbert scales.

Full Text (PDF) [156 KB]

Key words

quasi-solutions, regularization in Hilbert scales, convergence rates

AMS subject classifications

47A52, 65J20

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