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

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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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     author = {A. S. Leonov},
     title = {Which of inverse problems can have a~priori approximate solution accuracy estimates comparable in order with the data accuracy},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {339--348},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a2/}
}
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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/