Geodesic
Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 562-568 
A. S. Leonov. Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 562-568. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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).

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