Construction of a normal solution of non-linear ill-posed problems by the method of regularization
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 3, pp. 594-600
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A new way of choosing the regularization parameter when solving an ill-posed problem with approximately specified non-linear operator is described, based on a comparison of the discrepancy with an auxiliary functional (principle of discrepancy comparison). With the aid of this principle, convergence of the regularized solution to the normal solution (in the absence of uniqueness) is obtained for a wide class of normed spaces. Efficient algorithms are given for finding the regularization parameter in practical computations.
@article{ZVMMF_1979_19_3_a2,
author = {A. V. Baev},
title = {Construction of a normal solution of non-linear ill-posed problems by the method of regularization},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {594--600},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {1979},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a2/}
}
TY - JOUR AU - A. V. Baev TI - Construction of a normal solution of non-linear ill-posed problems by the method of regularization JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1979 SP - 594 EP - 600 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a2/ LA - ru ID - ZVMMF_1979_19_3_a2 ER -
%0 Journal Article %A A. V. Baev %T Construction of a normal solution of non-linear ill-posed problems by the method of regularization %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1979 %P 594-600 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a2/ %G ru %F ZVMMF_1979_19_3_a2
A. V. Baev. Construction of a normal solution of non-linear ill-posed problems by the method of regularization. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 3, pp. 594-600. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a2/