Geodesic
The critical level of discrepancy in regularization methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 6, pp. 1283-1297

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A class of methods of solving linear ill-posed problems in Hilbert space is studied. The regularization parameter is chosen from the condition for the norm of the discrepancy to be equal to the level of accuracy in specifying the right-hand side of the equation. This choice of regularization parameter leads in certain cases to a convergent order-wise optimal process, and in others to a divergent process. The case of an approximately specified operator is also considered. 
@article{ZVMMF_1983_23_6_a0,
     author = {G. M. Vainikko},
     title = {The critical level of discrepancy in regularization methods},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1283--1297},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_6_a0/}
}
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G. M. Vainikko. The critical level of discrepancy in regularization methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 6, pp. 1283-1297. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_6_a0/