Geodesic
On convergence rates for quasi-solutions of ill-posed problems
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 81-92
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.
Classification : 47A52, 65J20
Keywords: quasi-solutions, regularization in Hilbert scales, convergence rates 
@article{ETNA_2014__41__a20,
     author = {Neubauer,  Andreas and Ramlau,  Ronny},
     title = {On convergence rates for quasi-solutions of ill-posed problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {81--92},
     year = {2014},
     volume = {41},
     zbl = {1294.47019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a20/}
}
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Neubauer,  Andreas; Ramlau,  Ronny. On convergence rates for quasi-solutions of ill-posed problems. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 81-92. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a20/