This article is cited in 6 papers

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), 31 Kashirskoe shosse, Moscow, 115409, Russia

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.

Key words: linear inverse problems, correctness in the sense of Tikhonov, a priori and a posteriori accuracy estimate.

UDC: 517.397

Received: 05.12.2013
Revised: 29.01.2014

 English version: Numerical Analysis and Applications, 2014, 7:4, 284–292

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