Geodesic
The case a non self-conjugated problem with a posteriori choice of parameter regularization for implicit iteration method for solution of the linear equations with approximately operator
Trudy Instituta matematiki, Tome 22 (2014) no. 1, pp. 115-121 
O. V. Matysik. The case a non self-conjugated problem with a posteriori choice of parameter regularization for implicit iteration method for solution of the linear equations with approximately operator. Trudy Instituta matematiki, Tome 22 (2014) no. 1, pp. 115-121. http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The implicit iteration method for solution of the first-kind operator equations with a non self-conjugated bounded operator in the Hilbert space is proposed. Convergence of a method is proved in case of an a posteriori choice of number of iterations in ussual norm of Hilbert space, supposing that not only the right part of the equation but the operator as well have errors. The estimation of an error of method and estimation of a posteriori moment of stop are received.

[1] Matysik O. V., Savchuk V. F., “Iteratsionnaya protsedura neyavnogo tipa resheniya operatornykh uravnenii”, Dokl. NAN Belarusi, 53:6 (2009), 39–44

[2] Vainikko G. M., Veretennikov A. Yu., Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, M., 1986, 178 pp.

[3] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965, 520 pp.