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.
@article{SJVM_2012_15_1_a6,
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},
pages = {83--100},
publisher = {mathdoc},
volume = {15},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a6/}
}
TY - JOUR AU - A. S. Leonov TI - A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2012 SP - 83 EP - 100 VL - 15 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a6/ LA - ru ID - SJVM_2012_15_1_a6 ER -
%0 Journal Article %A A. S. Leonov %T A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2012 %P 83-100 %V 15 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a6/ %G ru %F SJVM_2012_15_1_a6
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/