This article is cited in 7 papers

Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?

A. S. Leonov

National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: For a linear operator equation of the first kind with perturbed data, it is shown that the global (on typical sets) a priori error estimate for its approximate solution can have the same order as that for the approximate data only if the operator of the problem is normally solvable. If the operator of the problem is given exactly, this is possible only if the problem is well-posed (stable).

Key words: regularization of ill-posed problems, a priori error estimation, normally solvable operator.

UDC: 519.642.8

Received: 21.10.2013

DOI: 10.7868/S0044466914040115

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:4, 575–581

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