Geodesic
A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 1, pp. 83-100

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A new scheme of a posteriori accuracy estimation for approximate solutions of ill-posed inverse problems is presented along with an algorithm of calculating this estimation. A new notion of extra-optimal regularizing algorithm is introduced as a method for solving ill-posed inverse problems having optimal in order a posteriori accuracy estimation. Sufficient conditions of extra-optimality are formulated and an example of extra-optimal regularizing algorithm is given. The developed theory is illustrated by numerical experiments. 
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     author = {A. S. Leonov},
     title = {A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a6/}
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A. S. Leonov. A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 1, pp. 83-100. http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a6/