Geodesic
Which of inverse problems can have a priori approximate solution accuracy estimates comparable in order with the data accuracy
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 339-348 
A. S. Leonov. Which of inverse problems can have a priori approximate solution accuracy estimates comparable in order with the data accuracy. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 339-348. http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a2/
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     title = {Which of inverse problems can have a~priori approximate solution accuracy estimates comparable in order with the data accuracy},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a priori global accuracy estimate for approximate solutions to linear inverse problems with perturbed data can be of the same order as approximate data errors for well-posed in the sense of Tikhonov problems only. A method for assessing the quality of selected sets of correctness is proposed. The use of the generalized residual method on a set of correctness allows us to solve the inverse problem and to obtain a posteriori accuracy estimate for approximate solutions, which is comparable with the accuracy of the problem data. The approach proposed is illustrated by a numerical example.

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