Which of inverse problems can have a priori approximate solution accuracy estimates comparable in order with the data accuracy
A. S. Leonov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Moscow, Kashirskoe shosse, 31
Keywords: linear inverse problems, correctness in the sense of Tikhonov, a priori and a posteriori accuracy estimate
Abstract
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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