A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 238-249
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We consider an operator equation of the first kind with error in the operator and in the right-hand side of the equation. The method is a function of this operator depending on a positive parameter $\alpha$. A lower estimate of a method of solving this equation for any value of $\alpha$ is obtained. A regularizing method based on Lavrent'ev's method is constructed, and a two-sided error estimate is obtained for this method. Discrete approximations of Lavrent'ev's method are constructed. Error estimates are obtained for these approximations. The discrete approximations were further used for a perturbation of the operator in the equation.
Keywords:
operator equation; regularization; error estimation; ill-posed problem.
@article{TIMM_2015_21_1_a24,
author = {V. P. Tanana and A. I. Sidikova},
title = {A two-sided error estimate for a regularizing method based on {M.M.} {Lavrent'ev's} method},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {238--249},
publisher = {mathdoc},
volume = {21},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a24/}
}
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V. P. Tanana; A. I. Sidikova. A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 238-249. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a24/